Finding cosmic voids and filament loops using topological data analysis

Apr 24, 2020 - 3:00 pm to 4:00 pm
Speaker
Elise Darragh-Ford (KIPAC) via zoom

Join us this Friday, April 24th at 3pm exclusively on zoom for the next meeting of the Stats and ML Journal Club. This week, Elise Darragh-Ford will lead a discussion on cosmic void finding with Topological Data Analysis. See you then!

Title: Finding cosmic voids and filament loops using topological data analysis
Abstract: We present a method called Significant Cosmic Holes in Universe (SCHU) for identifying cosmic voids and loops of filaments
in cosmological datasets and assigning their statistical significance using techniques from topological data analysis. In particular,
persistent homology is used to find different dimensional holes. For dark matter halo catalogs and galaxy surveys, the 0-, 1-, and 2-
dimensional holes can be identified with connected components (i.e. clusters), loops of filaments, and voids. The procedure overlays
dark matter halos/galaxies on a three-dimensional grid, and a distance-to-measure (DTM) function is calculated at each point of
the grid. A nested set of simplicial complexes (a filtration) is generated over the lower-level sets of the DTM across increasing
threshold values. The filtered simplicial complex can then be used to summarize the birth and death times of the different dimension
homology group generators (i.e., the holes). Persistent homology summary diagrams, called persistence diagrams, are produced
from the dimension, birth times, and death times of each homology group generator. Using the persistence diagrams and bootstrap
sampling, we explain how p-values can be assigned to each homology group generator. The homology group generators on a
persistence diagram are not, in general, uniquely located back in the original dataset volume so we propose a method for finding
a representation of the homology group generators. This method provides a novel, statistically rigorous approach for locating
informative generators in cosmological datasets, which may be useful for providing complementary cosmological constraints on the
effects of, for example, the sum of the neutrino masses. The method is tested on a Voronoi foam simulation, and then subsequently
applied to a subset of the SDSS galaxy survey and a cosmological simulation. Lastly, we calculate Betti functions for two of the
MassiveNuS simulations and discuss implications for using the persistent homology of the density field to help break degeneracy
in the cosmological parameters.