deletions | additions       diff --git a/Estimating coupling functions from phases.tex b/Estimating coupling functions from phases.tex  index 3e0fbb9..4c2295d 100644  --- a/Estimating coupling functions from phases.tex  +++ b/Estimating coupling functions from phases.tex 
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In total we selected $2753$ time traces with a minimum duration of $24h$ and at least two divisions. These gave $208'762$ velocities for each function. The data density (number of data points per discrete position in the phase plane) is shown in Figure \ref{fig:dataDensity}. An example of reconstructed functions from synthetic data is also shown in Figure \ref{fig:example_of_reconstructed_coupling_functions}.  In order to fully specify the model, the phase diffusion coefficients and the intrinsic frequencies values have to be provided in addition to the coupling functions. We also noticed by fitting synthetic data that the amplitude of the coupling functions was often reduced after the inference. Thus we fitted these parameters using a previously developed method \cite{bieler2014}, as well as multiplicative amplitude parameter in front of each coupling function, function to account of the loss of amplitude,  such that the model is able to faithfully reproduce the data (Figure \ref{fig:dataAndModelComparison}). The two final coupling functions (Figure \ref{fig:estimatedCouplingFunctions}) show that the inferred coupling is predominantly from the cell cycle to the circadian clock, as we previously described. The function $F_1$ shows an acceleration of the circadian clock around the division when the division take place before the circadian peak, consistent with our previous observations (Figure \ref{fig:estimatedCouplingFunctions}A, yellow). In addition we find two new interaction regions where the circadian clock is slowed down by the cell cycle (Figure \ref{fig:estimatedCouplingFunctions}A, blue). These regions were sometimes found by our previous inference method, but were not consistently positioned in the phase plane.