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\subsection{Initial values}  $ x(0) = 0 \quad b(0) = 1 \quad r(0) = 0 \quad \tilde{r}(0) = 0 \quad \tilde{b}_R(0) = 1$ \subsection{Universal values}  These values are presumably consistent between experiments: $\Gamma_0$, $\Gamma_1$ and $f$.  \subsection{