deletions | additions       diff --git a/res_fitting.md b/res_fitting.md  index 77d9e1f..97c74d8 100644  --- a/res_fitting.md  +++ b/res_fitting.md 
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### Signal fitting  The function used for fitting Ca2+ release events is shown on Figure \ref{fig:f2}. The shape of the function is described by 4 parameters: amplitude (\(A\)), rise and decay time constants (\(\tau_{rise},\tau_{decay}\)) and plateau duration (\(d\)). An additional parameter (\(\mu\)) determines the time when the maximum is reached. For the optimizer to obtain good performance when fitting the function used for fitting should be continously differentiable. The original fitting function: function describing a transient is:  \[  g(A, d, \tau_{d}, \tau_{r}, \mu, t) =   A\cdot\left\{  
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\exp\left( -\frac{t-\mu}{\tau_d}\right)\cdot\left(1-\exp(-2)\right)& \quad t\ge\mu+d  \end{array} \right.  \]  is convolved with a gaussian \(G(\sigma)\) to yield the actual fitting function:  \[  f(A, d, \tau_{d}, \tau_{r}, \mu, t, \sigma) = g \ast G  \]  For notational purposes we shall represent the fit funcion function  parameters by \(\mathbf{p}=\left[A,d,\tau{d},\tau_{r},\mu\right]\). The smoothing parameter \(\sigma\) will be fixed for all pixels. Therefore, for the *i*-th pixel the *k*-th event is represented by \(f(\mathbf{p}_{i,k},t)\). The entire raw signal for the *i*-th pixel is:  \[ 
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Because it is not know which part of the signal is the event and which is the baseline the first fit also has to estimate the baseline properties.  Signal in the candidate region is fitted with an extended fit function (Figure \ref{fig:fig2}) that also depends on relaxation baseline \(B\) and baseline offset \(C\). The \(C\) parameter allows for the possibility of an elevated background before the release event.   After paramater optimization with the extended fit function the same signal is fitted with a line. For both models the corrected Akaike Information Criterion (AICc \cite{Burnham_2004}) is calculated and the region is accepted only if the AICc for the fit function is less than the AICc for the line. This ensures that the goodness of the fit obtained with the fit function justifies the use of a more complicated model.