$\nu_{\alpha,\beta}$ via , $\pi_{\alpha}$ via  and $\PP_{\partial B_{\beta} \cap
            \partial B_{\alpha}}$ via .

    -   Select an edge $\partial B_{\beta'} \cap \partial
          B_{\alpha}$ of $B_{\alpha}$ with probability proportional to $\PP_{\partial B_{\beta'} \cap
            \partial B_{\alpha}}$.

    -   Pick a point $\zz_{\beta',\alpha}^{k}$ with uniform probability from the databank of re-entry points on edge $\partial B_{\beta'} \cap \partial
          B_{\alpha}$, and set $$\label{eq:reinject}
          \zz_{\alpha}(t+\mathit{\Delta} t) = \zz_{\beta',\alpha}^{k}$$

-   Go to step (1) and iterate to collect statistics.

In essence, the algorithm above is the same as the one proposed in Ref. , though the two differ in the details. For instance, we use a single set of cells instead of two (in Refs.  two staggered sets were used to ensure stability, but we observed no such stability problems with the procedure above). Besides a set of trajectories, one of the output of the procedure is to give the probability $\pi_\alpha$ to find the system in cell $B_\alpha$ at statistical steady state (see ). Indeed the computation of $\pi_{\alpha}$ was the main objective in Refs. . Below we will show how to extract more from the procedure, in particular reaction rate information, by appropriate modifications. Before getting there, however, let us make a few remarks about the 