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\section{Introduction}  \label{sec:Introduction}  - general \textit{General  introduction on the clock and cell cycle}  The circadian clock and the cell  cycle oscillators represent two cellular processes having a period in the range of one day.   At the single-cell level, the circadian rhythm is carried out by a network of transcriptional and translational feedback loops that drive rhythmic expression of genes with a period of about 24 hours. (ref) This cell autonomous rhythm is self-sustained (ref) and is considered to temporally orchestrate many important cell physiological processes such as metabolism (ref,ref), redox balance (ref) and chromatin landscapes/conformation (ref), {find other ph. Processes}.  The cell cycle can also be considered as a periodic process lasting on the order of one day in dividing mammalian cells (ref). Consequently, is reasonable to expect that, when circadian and cell cycles run in parallel in the same cell, their coupling could lead to synchronization.  - quick summary \textit{Observation  of what we did interaction between the two cycles in different cells}  Amplyfing (work in progress)  Observations of circadian variations in mitotic indices  in mammalian cells and on the daytime-dependence of cell division in mouse liver have led to the hypothesis that  the previous paper circadian cycle might gate cell-cycle progression.  \textit{Introduction on model - \textbf{JON, WHERE DO YOU WANT TO PLACE THIS SUBCHAPTER?} }   \textit{}Interest of this topic  Amplyfing (work in progress)  A deeper understanding of how the two biological systems interact is currently of great interest, notably to better understand the role of circadian clocks in proliferating tissues such as the epidermis, immune or stem cells (ref).  \textit{Our previous findings}  Amplyfing (work in progress)  In a previous work (ref), we performed a systematic analysis based on time-lapse imaging of circadian cycles in dividing mammalian NIH3T3 cells. This study clearly indicated that both oscillators tick in a tightly synchronized state. Moreover, contrary to our expectations, we unambiguously showed that the cell cycle progression exerts a unilateral influence on the circadian clock, and not the opposite.  - general introduction on modeling (dimensionality reduction, stochastic model)  \textit{Our new findings}  Amplyfing (work in progress)  In this follow-up study we further analyzed the dynamics of the two interacting oscillators by applying probabilistic inference. By developing signal-processing methods we indeed reconstructed the full stochastic dynamics of this interaction. This analysis allowed us to make more specific predictions on distinct cell cycle events that might have effects on the circadian clock, such the condensation of chromosomes starting from prophase during mitosis. We then eventually tested those prediction using further markers of cell cycle events.  \textbf{JON, WHERE DO YOU WANT TO PLACE THIS SUBCHAPTER?}  $\textrm{d}\theta = 2\pi /{T_1} \textrm{d}t + f_1(\theta) + F_1(\theta,\phi) \textrm{d}t + \sigma_1 \textrm{d} W^1_t $  $\textrm{d}\phi = 2\pi /{T_2} \textrm{d}t + f_2(\phi) + F_2(\theta,\phi) \textrm{d}t + \sigma_2 \textrm{d} W^2_t $