R. Badii

Complexity as Unpredictability of the Scaling Dynamics

The problem of quantifying complexity is discussed in the framework of a hierarchical modelling of physical systems. The dynamics underlying the formation of one-dimensional symbolic patterns is unfolded by using variable-length prefix-free codewords and described by means of allowed transitions on a logic tree. The derived model is employed to make predictions on the scaling behaviour of the systems observables at each level of resolution. The complexity of the system, relative to the unfolding scheme, is evaluated through a generalization of the information gain by comparing prediction and observation.

Refined scaling hypothesis for anomalously diffusing processes

Anomalous diffusion in artificial and natural stochastic processes is studied through the statistics of small-scale fluctuations. It is shown that the moments of certain locally averaged quantities, such as the square or absolute increments, do not scale like power laws, as generally assumed. A much improved scaling function is deduced, in analogy with a procedure first applied to nearest-neighbour dimension estimators. Extremely accurate determination of the scaling exponents is thus possible. Our refined formula is immediately applicable to the analysis of time series in turbulence, physiology, or economics.