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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

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

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…

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…

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

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

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

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

The results of the Anomalous Diffusion Challenge (AnDi Challenge) have shown that machine learning methods can outperform classical statistical methodology at the characterization of anomalous diffusion in both the inference of the…

Machine Learning · Computer Science 2023-01-18 Nicolás Firbas , Òscar Garibo-i-Orts , Miguel Ángel Garcia-March , J. Alberto Conejero

Biophysical processes within living systems rely on encounters and interactions between molecules in complex environments such as cells. They are often described by anomalous diffusion transport. Recent advances in single-molecule…

Data Analysis, Statistics and Probability · Physics 2025-02-27 Solomon Asghar , Ran Ni , Giorgio Volpe

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

While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at…

Machine Learning · Computer Science 2024-10-23 Jaeyong Bae , Yongjoo Baek , Hawoong Jeong

Anomaly detection, the technique of identifying abnormal samples using only normal samples, has attracted widespread interest in industry. Existing one-model-per-category methods often struggle with limited generalization capabilities due…

Computer Vision and Pattern Recognition · Computer Science 2024-07-03 Jiawei Zhan , Jinxiang Lai , Bin-Bin Gao , Jun Liu , Xiaochen Chen , Chengjie Wang

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

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

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

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

In order to characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine learning method to characterize…

Soft Condensed Matter · Physics 2023-11-29 Borja Requena , Sergi Masó , Joan Bertran , Maciej Lewenstein , Carlo Manzo , Gorka Muñoz-Gil

Diffusion models (DMs) have emerged as a powerful class of generative AI models, showing remarkable potential in anomaly detection (AD) tasks across various domains, such as cybersecurity, fraud detection, healthcare, and manufacturing. The…

Machine Learning · Computer Science 2025-02-28 Jing Liu , Zhenchao Ma , Zepu Wang , Chenxuanyin Zou , Jiayang Ren , Zehua Wang , Liang Song , Bo Hu , Yang Liu , Victor C. M. Leung

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
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