deletions | additions       diff --git a/Hidden Markov Models.tex b/Hidden Markov Models.tex  index 3fb77fd..aa2e9a4 100644  --- a/Hidden Markov Models.tex  +++ b/Hidden Markov Models.tex 
...
The HMM for inferring the cell cycle phase $\phi$ is very similar to the one for the circadian phase. The only difference is that we didn't included a baseline state, as it wasn't needed. The full HMM for the is defined by:  \begin{align*}   \label{eq:cellcylce_HMM} \begin{equation} \label{eqn:cellcylce_HMM}  \textrm{d}\phi_t = \frac{2\pi}{T_2}\textrm{d}t + \sigma_{\phi}\textrm{d}W_t  \end{equation}  \begin{equation} \label{eqn:cellcylce_HMM2}  \textrm{d}\alpha_t = -\gamma_{\alpha} (\alpha_t-\mu_{\alpha}) \textrm{d}t + \sigma_{\alpha}\textrm{d}W_t  \end{equation}  \begin{equation} \label{eqn:cellcylce_HMM3}  a_t = \exp(\alpha_t) w(\phi_t) +\xi  \end{equation}  %\begin{align*}   %\label{eq:cellcylce_HMM}  %\textrm{d}\phi_t  =& \frac{2\pi}{T_2}\textrm{d}t + \sigma_{\phi}\textrm{d}W_t\\ \textrm{d}\alpha_t %\textrm{d}\alpha_t  =& -\gamma_{\alpha} (\alpha_t-\mu_{\alpha}) \textrm{d}t + \sigma_{\alpha}\textrm{d}W_t\\ s_t %s_t  =& \exp(\alpha_t) w(\phi_t) +\xi\\ \end{align*} %\end{align*}  We used a mean period $T_2$ of $22$h and a phase diffusion coefficient $\sigma_{\phi}$ of $0.15$ $\textrm{rad} \; h^{-1/2}$. For the amplitude $\alpha$ we used a timescale $\gamma_{\alpha}^{-1}$ of $30$h a zero mean value $\mu_{\alpha}$ and a diffusion coefficient $\sigma_{\alpha}$ of $0.035$. The variance of the noise $\xi$ was set to $0.1$. The data were quantile-normalized as in previous section.