TY - JOUR A1 - Thapa, Samudrajit A1 - Wyłomańska, Agnieszka A1 - Sikora, Grzegorz A1 - Wagner, Caroline E. A1 - Krapf, Diego A1 - Kantz, Holger A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories JF - New Journal of Physics N2 - Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations. KW - diffusion KW - anomalous diffusion KW - large-deviation statistic KW - time-averaged mean squared displacement KW - Chebyshev inequality Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/abd50e SN - 1367-2630 VL - 23 PB - Dt. Physikalische Ges. ; IOP CY - Bad Honnef ; London ER - TY - GEN A1 - Thapa, Samudrajit A1 - Wyłomańska, Agnieszka A1 - Sikora, Grzegorz A1 - Wagner, Caroline E. A1 - Krapf, Diego A1 - Kantz, Holger A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1118 KW - diffusion KW - anomalous diffusion KW - large-deviation statistic KW - time-averaged mean squared displacement KW - Chebyshev inequality Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-493494 SN - 1866-8372 IS - 1118 ER - TY - JOUR A1 - Sandev, T. A1 - Iomin, Alexander A1 - Kantz, Holger A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Comb Model with Slow and Ultraslow Diffusion JF - Mathematical modelling of natural phenomena N2 - We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process. KW - comb-like model KW - anomalous diffusion KW - mean squared displacement KW - probability density function Y1 - 2016 U6 - https://doi.org/10.1051/mmnp/201611302 SN - 0973-5348 SN - 1760-6101 VL - 11 SP - 18 EP - 33 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Sandev, Trifce A1 - Chechkin, Aleksei V. A1 - Kantz, Holger A1 - Metzler, Ralf T1 - Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel JF - Fractional calculus and applied analysis : an international journal for theory and applications N2 - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed. KW - continuous time random walk (CTRW) KW - Fokker-Planck-Smoluchowski equation KW - Mittag-Leffler functions KW - anomalous diffusion KW - multi-scaling Y1 - 2015 U6 - https://doi.org/10.1515/fca-2015-0059 SN - 1311-0454 SN - 1314-2224 VL - 18 IS - 4 SP - 1006 EP - 1038 PB - De Gruyter CY - Berlin ER - TY - JOUR A1 - Godec, Aljaz A1 - Chechkin, Aleksei V. A1 - Barkai, Eli A1 - Kantz, Holger A1 - Metzler, Ralf T1 - Localisation and universal fluctuations in ultraslow diffusion processes JF - Journal of physics : A, Mathematical and theoretical N2 - We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD. KW - Sinai diffusion KW - anomalous diffusion KW - quenched energy landscape Y1 - 2014 U6 - https://doi.org/10.1088/1751-8113/47/49/492002 SN - 1751-8113 SN - 1751-8121 VL - 47 IS - 49 PB - IOP Publ. Ltd. CY - Bristol ER -