Before revision:   We show that TDA can accurately map out phase diagrams for interacting particles with varying adhesion and self-propulsion , at constant population size as well as when proliferation is permitted.
After revision:  We show that these topological loops (i.e. dimension 1 homology) are robust to variations in particle number and density, particularly in comparison to connected components (i.e. dimension 0 homology). We use TDA to map out phase diagrams for interacting particles with varying adhesion and self-propulsion , at constant population size as well as when proliferation is permitted.