deletions | additions       diff --git a/Hidden Markov Models.tex b/Hidden Markov Models.tex  index de4b26c..b0813c7 100644  --- a/Hidden Markov Models.tex  +++ b/Hidden Markov Models.tex 
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The transition probability for the phase and the emission probability are given by simple Normal distributions, and the transition probability for the two Ornstein-Uhlenbeck processes is given by a Normal distribution with mean $\mu_{\lambda} + \exp(-\gamma_{\lambda}\Delta t)(\lambda_t - \mu_{\lambda})$ and variance $\sigma_{\lambda}^2 / (2\gamma_{\lambda} )(1-\exp(-2\gamma_{\lambda}\Delta t))$\cite{Lemons2002}.  We preprocessed the data by quantile-normalizing each trace, i.e.  the signal $s_t$ was rescaled by subtracting it's quantile $p$ and dividing by it's quantile $1-p$ with $p = 0.05$. This is very similar to normalizing the signal between $0$ and $1$ but is more robust to noise. robust.  Because of this all the parameters related to the signal have arbitrary units. We also masked the typical dip in the signal at division to avoid spurious deformation of the circadian phase at division. \subsubsection{Cell cycle, nuclear area}