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Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.
Recently, a large number of research teams from around the world collaborated in the so-called 'anomalous diffusion challenge'. Its aim: to develop and compare new techniques for inferring stochastic models from given unknown time series, and estimate the anomalous diffusion exponent in data. We use various numerical methods to directly obtain this exponent using the path increments, and develop a questionnaire for model selection based on feature analysis of a set of known stochastic processes given as candidates. Here, we present the theoretical background of the automated algorithm which we put for these tasks in the diffusion challenge, as a counter to other pure data-driven approaches.