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\subsection{A phase model for the coupling between the circadian and cell cycles}  Overall our phase model is able to recapitulate most of the features present in the data. It explains the observed synchrony in the data by an interplay between the effect of the $F_1$ coupling function and the phase diffusion coefficients, giving a of mean  circadian phase at division around $0.75 \times 2\pi$. The deterministic model allows to predict the existence , and estimate the position, of higher order attractors. While we found signs of $2:1$ mode-locking in our dataset, we found it is difficult to assess other mode-locked states with recording durations of about three days. Indeed the presence of noise in the dynamic renders difficult to distinguish between a temporary excursion away from the $1:1$ attractor and genuine phase locking around a different one. Finally it is remarkable that we are able to observe the phase shifts between the two oscillators in function of the intrinsic period difference, a clear mark that the two oscillators are in resonance.   \subsection{Coupling directionality} 
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In this work we developed a novel method (TODO:true?) of inferring phases from data using hidden Markov models. We found that this method is adequate to decode real-world data, as it allows to specify a noise model as well as the underlying dynamic of the hidden states, and to explicitly take into account features of the data like amplitude, making the hypothesis underlying the analysis more manifest. A consequence of this is that several parameters have to be calibrated. Note however that because we learn the waveform, linking the phase to the data, from a large collection of time traces, our inferred phase is robust to transformations of the data, unlike methods based on the Hilbert transform \cite{Kralemann_2008}.  \subsection{Phase dynamics reconstruction as a general tool for system biology} \subsection{Conclusion}  ?