Errata for the paper "Anisotropic Gaussian Mutations for Metropolis Light Transport through Hessian-Hamiltonian Dynamics"

The $\alpha > 0$ case in Equation (16) in the paper should read:
$$ \left(\frac{\exp\left(\sqrt{\alpha}T \right) - \exp\left(-\sqrt{\alpha}T\right)}{2\sqrt{\alpha}}\right) \hat{p}\left(0 \right) \\ \qquad + \frac{\beta}{2\alpha}\left(\exp\left(\sqrt{\alpha}T\right) + \exp\left(-\sqrt{\alpha}T\right) - {\color{Red} 2}\right), $$ instead of $$ \left(\frac{\exp\left(\sqrt{\alpha}T \right) - \exp\left(-\sqrt{\alpha}T\right)}{2\sqrt{\alpha}}\right) \hat{p}\left(0 \right) \\ \qquad + \frac{\beta}{2\alpha}\left(\exp\left(\sqrt{\alpha}T\right) + \exp\left(-\sqrt{\alpha}T\right) - 1\right). $$

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Also, Equation (18) in the paper should read:
$$ S = \sum_{i=1}^{N} s_{i} \boldsymbol{e}_{i} {\color{red} \boldsymbol{v}_{i}^T}, \; \boldsymbol{o} = \sum_{i=1}^{N} o_{i} \boldsymbol{e}_{i}, $$ where $\boldsymbol{v}_{i}$ is a $N$-dimensional vector whose $i$-th component is $1$ and the other components are $0$, instead of $$ S = \sum_{i=1}^{N} s_{i} \boldsymbol{e}_{i}, \; \boldsymbol{o} = \sum_{i=1}^{N} o_{i} \boldsymbol{e}_{i}. $$

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Finally, Equation (23) in the paper should read:
$$ A = \sum_{i=1}^{N} \begin{cases} \frac{1}{\left| \lambda^{H}_{i} \right|}\boldsymbol{e}^{H}_{i} {\color{Red} {\boldsymbol{e}^{H}_{i}}^T} & \mbox{if } \lambda^{H}_{i} \neq 0 \\ 0 & \mbox{otherwise}, \end{cases} $$ instead of $$ A = \sum_{i=1}^{N} \begin{cases} \frac{1}{\left| \lambda^{H}_{i} \right|}\boldsymbol{e}^{H}_{i} & \mbox{if } \lambda^{H}_{i} \neq 0 \\ 0 & \mbox{otherwise}. \end{cases} $$