Monotonic decay of persistence-diagram strength

Determine whether the L1-norm of the persistence diagram of V_p is always no larger than that of V_q for every pair of parameters 1≤p≤q, equivalently whether the combined strength of the equilibria monotonically decreases as the parameter increases.

Background

The paper disproves a monotonicity conjecture concerning the number of equilibria of the parameterized potentials V_p by exhibiting a configuration for which V_1 has more index-1 equilibria than V_p for sufficiently large p.

The authors propose a weaker question based on persistence diagrams: although the number of equilibria may increase, their aggregate persistence strength might still decrease monotonically with the parameter.