Stochastic optimization for the calculation of the optimal critical curve from experimental data in a model of the process of regaining balance after perturbation from quiet stance

We demonstrate the successful application of ALOPEX stochastic optimization to the problem of calculating the optimal critical curve in a dynamical systems model of the process of regaining balance after perturbation from quiet stance. Experimental data provide the time series of angles for which the subjects were able to regain balance after an initial perturbation. The optimal critical curve encloses all data points and has a minimum distance from the border points of the data set. We demonstrate the results of the optimization firstly using the traditional cost function of chi-square distance. We then successfully introduce a modified cost function that fits the model to the experimental data by taking into account the specific requirements of the model. By use of the proposed cost function, combined with the efficiency of our optimization method, an optimal critical curve is calculated even in the cases of very asymmetric data sets that lie within the capabilities of the existing model.