deletions | additions       diff --git a/Hidden Markov Models.tex b/Hidden Markov Models.tex  index 9d7a216..063d38c 100644  --- a/Hidden Markov Models.tex  +++ b/Hidden Markov Models.tex 
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The complete HMM for the circadian clock is defined by:  \begin{align*}   \label{eq:circ_HMM}  \textrm{d}\theta_t =& \frac{2\pi}{T_1}\textrm{d}t + \sigma_{\theta}\textrm{d}W_t\\  \textrm{d}\lambda_t =& -\gamma_{\lambda} (\lambda_t-\mu_{\lambda}) \textrm{d}t + \sigma_{\lambda}\textrm{d}W_t\\  \textrm{d}B_t =& -\gamma_{B} (B_t-\mu_{B}) \textrm{d}t + \sigma_{B}\textrm{d}W_t\\ 
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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}  \textrm{d}\phi_t =& \frac{2\pi}{T_2}\textrm{d}t + \sigma_{\phi}\textrm{d}W_t\\  \textrm{d}\alpha_t =& -\gamma_{\alpha} (\alpha_t-\mu_{\alpha}) \textrm{d}t + \sigma_{\alpha}\textrm{d}W_t\\  s_t =& \exp(\alpha_t) w(\phi_t) +\xi\\