deletions | additions       diff --git a/Estimating coupling functions from phases.tex b/Estimating coupling functions from phases.tex  index 1131acb..1d7bdf8 100644  --- a/Estimating coupling functions from phases.tex  +++ b/Estimating coupling functions from phases.tex 
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%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 usually reduced after the inference. Thus we fitted these four  parameters using a previously developed method \cite{bieler2014}, as well as multiplicative amplitude parameter in front of each coupling function to account of the loss of amplitude, such that the model is able to faithfully reproduce the data (Figure \ref{fig:dataAndModelComparison}). \ref{fig:dataAndModelComparison}, Section \ref{sec:stochasticModel}).  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 just after the division when the division take place in a circadian window that extend from $\theta \approx 0.5$ to $0.75 \times 2\pi$, consistent with our previous observations (Figure \ref{fig:estimatedCouplingFunctions}A, yellow). In addition we found 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.