scholarly journals Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

2014 ◽  
Vol 16 (44) ◽  
pp. 24128-24164 ◽  
Author(s):  
Ralf Metzler ◽  
Jae-Hyung Jeon ◽  
Andrey G. Cherstvy ◽  
Eli Barkai
Keyword(s):  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Diffusion Processes ◽  
Diffusion Models ◽  
Single Particle Tracking ◽  
Diffusion Data

This Perspective summarises the properties of a variety of anomalous diffusion processes and provides the necessary tools to analyse and interpret recorded anomalous diffusion data.

Unsupervised learning of anomalous diffusion data an anomaly detection approach

2021 ◽  
Author(s):  
Gorka Muñoz-Gil ◽  
Guillem Guigo i Corominas ◽  
Maciej Lewenstein
Keyword(s):  
Anomalous Diffusion ◽  
Diffusion Processes ◽  
Theoretical Models ◽  
Diffusion Models ◽  
Supervised Machine Learning ◽  
Machine Learning Techniques ◽  
Physical Parameters ◽  
Diffusion Data ◽  
Detection Approach ◽  
Physical Phenomena

Abstract The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to describe such processes, but their application to experimental setups is often challenging, due to the stochastic nature of the phenomena and the difficulty to harness reliable data. The latter often consists on short and noisy trajectories, which are hard to characterize with usual statistical approaches. In recent years, we have witnessed an impressive effort to bridge theory and experiments by means of supervised machine learning techniques, with astonishing results. In this work, we explore the use of unsupervised methods in anomalous diffusion data. We show that the main diffusion characteristics can be learnt without the need of any labelling of the data. We use such method to discriminate between anomalous diffusion models and extract their physical parameters. Moreover, we explore the feasibility of finding novel types of diffusion, in this case represented by compositions of existing diffusion models. At last, we showcase the use of the method in experimental data and demonstrate its advantages for cases where supervised learning is not applicable.

scholarly journals Probing the type of anomalous diffusion with single-particle tracking

2014 ◽  
Vol 16 (17) ◽  
pp. 7686-7691 ◽  
Author(s):  
Dominique Ernst ◽  
Jürgen Köhler ◽  
Matthias Weiss
Keyword(s):  
Random Walk ◽  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Single Particle Tracking ◽  
Tracking Data

We introduce a versatile method to extract the type of (transient) anomalous random walk from experimental single-particle tracking data.

scholarly journals High-Speed Single-Particle Tracking of GM1 in Model Membranes Reveals Anomalous Diffusion due to Interleaflet Coupling and Molecular Pinning

Nano Letters ◽  
2014 ◽  
Vol 14 (9) ◽  
pp. 5390-5397 ◽  
Author(s):  
Katelyn M. Spillane ◽  
Jaime Ortega-Arroyo ◽  
Gabrielle de Wit ◽  
Christian Eggeling ◽  
Helge Ewers ◽  
...  
Keyword(s):  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
High Speed ◽  
Single Particle Tracking ◽  
Model Membranes

scholarly journals Guidelines for the Fitting of Anomalous Diffusion Mean Square Displacement Graphs from Single Particle Tracking Experiments

PLoS ONE ◽  
2015 ◽  
Vol 10 (2) ◽  
pp. e0117722 ◽  
Author(s):  
Eldad Kepten ◽  
Aleksander Weron ◽  
Grzegorz Sikora ◽  
Krzysztof Burnecki ◽  
Yuval Garini
Keyword(s):  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Mean Square Displacement ◽  
Single Particle Tracking ◽  
Mean Square

scholarly journals Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 498
Author(s):  
Chen Zhang ◽  
Kevin Welsher
Keyword(s):  
Fisher Information ◽  
Particle Tracking ◽  
Single Particle ◽  
Biological Samples ◽  
Tracking System ◽  
Single Particle Tracking ◽  
Uniform Sampling ◽  
Single Dimension ◽  
3D Localization ◽  
Particle Localization

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

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