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.

Apr 24, 2020 - 3:00 pm to 4:00 pm

Speaker

Elise Darragh-Ford (KIPAC) via zoom