Crucial Event Rehabilitation Therapy by Bruce J. West & Paolo Grigolini & Mauro Bologna

Author:Bruce J. West & Paolo Grigolini & Mauro Bologna
Language: eng
Format: epub
ISBN: 9783031462771
Publisher: Springer International Publishing

The success of fractal modeling of biomedical ONs suggests that nature prefers fractal structures and fractal statistics over those generated by classical scaling. One reason why this may be true is that fractal processes are more adaptive to internal fluctuations as well as to fluctuations in the environment than are classical processes. In fact, West [139] constructed a simple quantitative model of error response to illustrate the difference between the response of classical and fractal model structures to random perturbations of the model parameters. Without going into the mathematical details, the relative errors of classical and fractal scaling with Gaussian fluctuations in the scaling parameters are graphed in Fig. 3.7. The growth of error associated with fluctuations in the parameter controlling the size of the diameter of the bronchial airway within two such models is shown as an exemplar.

Fig. 3.7 The relative error between model predictions of the size of a bronchial airway and the same prediction when the growth is corrupted by a noisy parameter. The noise is given by a Gaussian random process in both models. In the classical case the ratio of the perturbed and unperturbed airways grows as whereas the fractal model ratio grows as . The difference between the classical scaling model and the fractal scaling model is striking. From [139] with permission

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