  In arXiv:0909.0508 D-particle degeneracies were calculated using novel
methods. By analysing this refined computation of the index in the setting of
the topological B model, a correspondence is found between flow trees in the
supergravity description and B-branes in the topological theory. This enables
us to use the same refinement also for single flows. A concrete example will be
given, providing strong support for this method, while at the same time
confirming the prediction of a new elliptic genus in arXiv:0909.0508.
