Before revision:  which is quantified by equalities-involved permutation relative entropy in our nonlinear dynamics analysis of heart rates . Equal values are not rare in discrete heartbeats because of the limits of resolution of signals collection, and more importantly equal states contain underlying important cardiac regulation information which is neglected by the original permutative method and some measurements of time irreversibility .
After revision:  which is quantified by equalities-involved permutation relative entropy in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not rare in discrete heartbeats because of the limits of resolution of signals collection, and more importantly equal states contain underlying important cardiac regulation information which is neglected by the original permutative method and some measurements of time irreversibility .