TY  - JOUR
A1  - Vilk, Ohad
A1  - Aghion, Erez
A1  - Avgar, Tal
A1  - Beta, Carsten
A1  - Nagel, Oliver
A1  - Sabri, Adal
A1  - Sarfati, Raphael
A1  - Schwartz, Daniel K.
A1  - Weiß, Matthias
A1  - Krapf, Diego
A1  - Nathan, Ran
A1  - Metzler, Ralf
A1  - Assaf, Michael
T1  - Unravelling the origins of anomalous diffusion
BT  - from molecules to migrating storks
JF  - Physical Review Research
N2  - 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.
Y1  - 2022
U6  - https://doi.org/10.1103/PhysRevResearch.4.033055
SN  - 2643-1564
VL  - 4
IS  - 3
SP  - 033055-1
EP  - 033055-16
PB  - American Physical Society
CY  - College Park, MD
ER  - 
TY  - JOUR
A1  - Meyer, Philipp
A1  - Aghion, Erez
A1  - Kantz, Holger
T1  - Decomposing the effect of anomalous diffusion enables direct calculation of the Hurst exponent and model classification for single random paths
JF  - Journal of physics / Institute of Physics. A, Mathematical, nuclear and general
N2  - 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.
KW  - time-series analysis
KW  - decomposing anomalous diffusion
KW  - anomalous
KW  - diffusion exponent
KW  - process inference
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac72d4
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 27
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -