PMC

The figure shows the calculation of derivatives for the JAK2/STAT5 model for the dynamical variable pSTAT5 at minutes with respect to the parameter CISInh on the y-axis, for several values of the parameter CISInh on the x-axis. For finite difference approximation, (red), (blue) and (green) was used. The numerical errors rapidly become uncontrollable as gets smaller. For larger , finite difference approximation is of bad quality showing systematic errors. In contrast, the analytical derivatives calculated by the sensitivity equations produce stable and correct results (black).

Geometrical meanings of the three finite difference approximation methods.

a) The effect of the smoothing (N = 2; M = 3,11,15) on the velocity waveform is limited. (b,c) The impact of varying the filter width on the time derivative for the SG-D approach and the SG-S one severely impact on the velocity time derivative peak. (d) Varying the central finite difference order provides more stable approximation of the time derivative.

The Gaussian graphical model obtained from a finite difference approximation to the Poisson equation has only local spatial dependency (left panel) resulting in a pentadiagonal inverse covariance matrix (right panel).