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We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the Joseph effect [Mandelbrot 1968], fat-tails of the increment probability density lead to a Noah effect [Mandelbrot 1968], and non-stationarity, to the Moses effect [Chen et al. 2017]. After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled Levy walk, compare our results to theoretical predictions, and discuss the generality of the method.
A continuous Markovian model for truncated Levy random walks is proposed. It generalizes the approach developed previously by Lubashevsky et al. Phys. Rev. E 79, 011110 (2009); 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010) allowing for nonlinear
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structur
We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on the microtubule and their detachment rates. We fo
We decompose the anomalous diffusive behavior found in a model of aging into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau-Manneville map. The increments can
Levy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of non revisitable targets, we propose an alternative model of bidimensional search processes, which explicitly relies on