Before revision:  This also gives a second , very simple algorithm to compute the q-th persistent Laplacian . This in turn leads to a new algorithm to compute the q-th persistent Betti number for a pair of spaces which can be significantly more efficient than existing algorithmsunder some conditions .
After revision:  This also gives a second , very simple algorithm to compute the q-th persistent Laplacian which in turn leads to a new algorithm to compute the q-th persistent Betti number for a pair of spaces which can be significantly more efficient than existing algorithmsunder some conditions .