Before revision:  For a given particle configuration , topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology) , and can compare different particle configurations based on the "cost" of URLanizing one configuration into another.
After revision:  For a given particle configuration , topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology) and can compare different particle configurations based on the "cost" of URLanizing one configuration into another.