this trajectory is such that $S_i$ was the edge of cell $B_\alpha$ it hit last. We refer the reader to Ref.  for more details.

![ Contourplot of the Mueller potential with the 36 points (shown as grey dots) generating the Voronoi tessellation shown as grey lines. The reactant $A$ and product $B$ states are identified with cell $B_1$ and $B_{36}$, respectively. []{data-label="fig:potMull"}](fig4){width="3.25in"}

#### Illustrative example. {#illustrative-example. .unnumbered}

We end this note by illustrating our sampling procedure on the example of a system evolving by Langevin dynamics on a two-dimensional potential, i.e. $\zz(t)=(\xx(t),\vv(t))$, $\xx,\vv \in \RR^2$ and $$\label{eq:langevin}
  \begin{cases}
    \dot \xx(t) = \vv(t), \\
    \dot \vv(t) = - \nabla V(\xx(t)) - \gamma \vv(t) +
    \sqrt{2\beta^{-1}\gamma}\, \eeta(t).
  \end{cases}$$ Here $V(\xx)$ is the Mueller potential [@mueller] whose contourplot is shown in Fig. \[fig:potMull\], $\beta=1/(k_BT)$ is the inverse temperature and $\eeta(t)$ is a Gaussian white-noise with mean zero and covariance $\< \eta_i(t) \eta_j(t')\> = \delta_{ij}
\delta(t-t')$. $\gamma$ is the friction coefficient and, for simplicity, we have set the mass tensor to the identity. Below we took $\gamma=100$ and $\beta^{-1}=20$ (which is about $20\%$ the value of the energy barrier between the minimum at the top left corner of the Mueller potential and the saddle 