Final report of project "Anomalous transport in complex systems: stochastic modeling and statistical data analysis

In the first reference period of the project (September 2015 - February 2016) we derived a Gaussian-based stochastic model, in accordance with a heterogeneity assumption and compatible with the Fractional Diffusion Equation (FDE). The derived model belongs to the class generalized grey Brownian Motion (ggBM), associated with the time-space fractional diffusion equation. A numerical algorithm and software for numerical simulations was then developed and tested. In the second reference period of the project (March-June 2016) we investigated the best choice of of statistical indicators with the goal of having the best chances to select the best model to correctly interpret a set of experimental data and, in particular, single particle tracking in laboratory studies of biological transport, such as, e.g., the diffusion of macromolecules (proteins, lipids) in the cell cytoplasm or membrane. Thus, we implemented and tested the codes for the estimation of proper statistical indicators and we applied them to artificial data from numerical simulations of the model. Thus, we got a characterization, for different set of parameters, of the simulated trajectories in terms of the chosen statistical indicators.