Before revision:  We derive a self-consistent set of message passing equations that allow for fast computation of probability distributions in systems that contain short loops, potentially with high density, as well as  expressions for the entropy and partition function of such systems , which are notoriously difficult quantities to compute.
After revision:  We derive a self-consistent set of message passing equations that allow for fast computation of probability distributions in systems that contain short loops, potentially with high density, as well as giving expressions for the entropy and partition function of such systems , which are notoriously difficult quantities to compute.