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### Signal fitting  #### Fitting function for transients  The function used for fitting Ca2+ release events is shown on Figure \ref{fig:fit}. The shape of the function is described by 4 parameters: amplitude (\(A\)), rise and decay time constants (\(\tau_{r},\tau_{d}\)) 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 function describing a transient is: \[  g(A, d, \tau_{d}, \tau_{r}, \mu, t) =   A\cdot\left\{  
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The transient consists of four phases: zero level before the onset of the transient, an exponential increase with time constant \(\tau_r\) starging when \(t=\mu-2\tau_r\), a plateau phase of duration \(d\) starting at \(t=\mu\) and an exponential decay with time constant \(\tau_d\) starting at \(t=\mu+d\)   The For the optimizer to obtain good performance when fitting the function used for fitting should be continously differentiable. With this in mind, the  transient function is convolved with a gaussian \(G(\sigma)\) to yield the actual fitting function: \[  f(A, d, \tau_{d}, \tau_{r}, \mu, t, \sigma) = g \ast G  \]