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Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating…

Computer Vision and Pattern Recognition · Computer Science 2025-04-08 Yusef Ahsini , Marc Escoto , J. Alberto Conejero

The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…

Machine Learning · Computer Science 2025-04-01 Wenjie Cai , Yi Hu , Xiang Qu , Hui Zhao , Gongyi Wang , Jing Li , Zihan Huang

Understanding and identifying different types of single molecules' diffusion that occur in a broad range of systems (including living matter) is extremely important, as it can provide information on the physical and chemical characteristics…

Quantitative Methods · Quantitative Biology 2023-03-07 Patrycja Kowalek , Hanna Loch-Olszewska , Łukasz Łaszczuk , Jarosław Opała , Janusz Szwabiński

Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of diffusion states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes of…

Biological Physics · Physics 2024-01-24 Xiang Qu , Yi Hu , Wenjie Cai , Yang Xu , Hu Ke , Guolong Zhu , Zihan Huang

Anomalous diffusion, which shows a deviation of transport dynamics from the framework of standard Brownian motion, is involved in the evolution of various physical, chemical, biological, and economic systems. The study of such random…

Machine Learning · Computer Science 2021-09-21 Dezhong Li , Qiujin Yao , Zihan Huang

Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…

Machine Learning · Computer Science 2021-08-09 Òscar Garibo i Orts , Miguel A. Garcia-March , J. Alberto Conejero

The study of the dynamics of natural and artificial systems has provided several examples of deviations from Brownian behavior, generally defined as anomalous diffusion. The investigation of these dynamics can provide a better understanding…

Data Analysis, Statistics and Probability · Physics 2025-08-29 Carlo Manzo

Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in…

Data Analysis, Statistics and Probability · Physics 2021-06-21 Alessia Gentili , Giorgio Volpe

In recent years, the segmentation of short molecular trajectories with varying diffusive properties has drawn particular attention of researchers, since it allows studying the dynamics of a particle. In the past decade, machine learning…

Machine Learning · Computer Science 2026-01-19 Junwoo Park , Nataliya Sokolovska , Clément Cabriel , Ignacio Izeddin , Judith Miné-Hattab

When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled…

Statistical Mechanics · Physics 2024-10-21 Henrik Seckler , Ralf Metzler

The deviation from pure Brownian motion generally referred to as anomalous diffusion has received large attention in the scientific literature to describe many physical scenarios. Several methods, based on classical statistics and machine…

Countless systems in biology, physics, and finance undergo diffusive dynamics. Many of these systems, including biomolecules inside cells, active matter systems and foraging animals, exhibit anomalous dynamics where the growth of the mean…

Statistical Mechanics · Physics 2021-08-11 Aykut Argun , Giovanni Volpe , Stefano Bo

Anomaly detection is a fundamental task in machine learning and data mining, with significant applications in cybersecurity, industrial fault diagnosis, and clinical disease monitoring. Traditional methods, such as statistical modeling and…

Machine Learning · Computer Science 2025-05-09 Yi Chen

The life of a cell is governed by highly dynamical microscopic processes. Two notable examples are the diffusion of membrane receptors and the kinetics of transcription factors governing the rates of gene expression. Different fluorescence…

Quantitative Methods · Quantitative Biology 2020-04-03 Maxime Woringer , Ignacio Izeddin , Cyril Favard , Hugues Berry

Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…

Statistical Mechanics · Physics 2025-11-14 Alvaro Lanza , Xiang Qu , Stefano Bo

Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from…

Biological Physics · Physics 2025-12-10 Gongyi Wang , Yu Zhang , Zihan Huang

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…

Statistical Mechanics · Physics 2019-07-24 Stefano Bo , Falko Schmidt , Ralf Eichhorn , Giovanni Volpe

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…

Statistical Mechanics · Physics 2023-09-14 Henrik Seckler , Ralf Metzler

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a…

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. Deciphering the stochastic mechanism behind the recorded dynamics…

Statistical Mechanics · Physics 2023-09-14 Henrik Seckler , Janusz Szwabinski , Ralf Metzler
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