662 citations · 11.9k across the 197 of their papers we have counts for
203 papers
Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises
Z. Tomovski, K. Gorska, T. Pietrzak +2
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power…
Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
Henrik Seckler, Janusz Szwabinski, Ralf Metzler
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphe…
Time-fractional Caputo derivative versus other integro-differential operators in generalized Fokker-Planck and generalized Langevin equations
Qing Wei, Wei Wang, Hongwei Zhou +2
Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous diffusion in a large variety of complex systems. The equivalent formulations in terms o…
Non-Markovian gene expression
Ohad Vilk, Ralf Metzler, Michael Assaf
We study two non-Markovian gene-expression models in which protein production is a stochastic process with a fat-tailed non-exponential waiting time distribution (WTD). For both mo…
Minimal model of diffusion with time changing Hurst exponent
Jakub Slezak, Ralf Metzler
We introduce the stochastic process of incremental multifractional Brownian motion (IMFBM), which locally behaves like fractional Brownian motion with a given local Hurst exponent…
Modelling intermittent anomalous diffusion with switching fractional Brownian motion
Michał Balcerek, Agnieszka Wyłomańska, Krzysztof Burnecki +2
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In ad…