Figure 2

Illustration for the piece-wise definition of a function that maps parameter value to an index, over three distinct regimes. The solid line represents the simplified Gaussian functions as provided in the figure, in which the width parameter is defined so that the Index falls below 0.5 when the parameter value is less than 20 and greater than 60 and the “perfect” regime is between 30 and 40. The dotted lines illustrate linear functions that have equivalent “Index = 0.5” points as the Gaussian lines and the dashed lines illustrate linear functions that drop to zero at approximately the same points as the Gaussian lines. Note the lack of sharp “shoulders” in the Gaussian equations, in contrast to the linear functions.