After a brief review of several contexts where (BPS) invariants change as function of the external moduli, I will discuss how the use of Maxwell-Boltzmann statistics (as opposed to Bose-Fermi statistics) simplifies the problem of determining the change of the BPS spectrum. I will continue with explaining how the BPS invariant corresponding to a multi-center black hole can be determined using localization. Based on work with B. Pioline and A. Sen.