Optimizing with the van Pelt and Uylings method

An Octave (MATLAB compatible) script "vanpeltestimation.m" was created to facilitate the optimization of model parameters for any set of  morphological network data, such as that obtained by Ger Ramakers.

The second approach presented by van Pelt and Uylings (Brain and Mind, 2003) was found to be the most suitable to the information that is available.  In that method, parameters of the D(t) function are estimated first. That may be done here in two ways:

1. Regression to an exponential D(t) function (which may take the standard deviation  into account).
2. A polynomial fit followed by extracting parameters that can be used in an exponential D(t) function by comparing the polynomial function with the Taylor expansion of an exponential D(t) function.

There is an important remaining question: Does using an optimized van Pelt and Uylings exponential model function guarantee an improved match to real network development? The primary difference between their model and the use of a polynomial model is that the van Pelt and Uylings model (at least partially) phenomenological, while the polynomial model is entirely statistical. In terms of realism, the van Pelt and Uylings model takes into account in its optimization procedures the distribution of plausible development results. To achieve the same with the purely statistical model provided by a polynomial growth function, the polynomial model would have to be extended to fit probability distributions rather than simple means.