Jessi Cisewski-Kehe, University of Wisconsin-Madison
Authors: Jessi Cisewski-Kehe, Brittany T. Fasy, Wojciech Hellwing, Mark R. Lovell, Pawel Drozda, and Mike Wu
2022 AWM Research Symposium
Women in Computational Topology

Topological Data Analysis (TDA) is a beneficial technique for analyzing spatially complex web-like data such as the large-scale structure (LSS) of the Universe. The accepted cosmological model presumes cold dark matter but discriminating LSS under varying cosmological assumptions is of interest. Cosmologists develop large-scale simulations that allow for visualizing and analyzing the LSS under varying physical assumptions.  Each object in the 3D data set can represent structures such as dark matter halos, and topological summaries ("persistence diagrams") can be obtained for these simulated data that summarize the different dimensional holes in the data. Hypothesis tests using persistence diagrams provide a way to make more rigorous comparisons of LSS under different theoretical models. We present several possible test statistics for two-sample hypothesis tests using persistence diagrams, and carry out a simulation study to investigate the performance of the proposed test statistics using cosmological simulation data for inference on distinguishing LSS assuming cold dark matter versus a different cosmological model which assumes warm dark matter.

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