  We report here an extension of a previous work in which we have shown that
matrix models provide a tool to compute the intersection numbers of p-spin
curves. We discuss further an extension to half-integer p, and in more details
for p=1/2 and p=3/2. In those new cases one finds contributions from the Ramond
sector, which were not present for positive integer p.The existence of Virasoro
constraints, in particular a string equation, is considered also for
half-integral spins. The contribution of the boundary of a Riemann surface, is
investigated through a logarithmic matrix model The supersymmetric random
matrices provide extensions to mixed positive and negative p punctures.
