Characterization of diffusion processes: Normal and anomalous regimes

Alves, Samuel B.; Oliveira, Gilson F. de; Oliveira, L. C. de; Silans, Thierry Passerat de; Chevrollier, Martine; Oriá, Marcos; Cavalcante, Hugo L. D. de S.

doi:10.1016/j.physa.2015.12.049

Cited by 38 publications

(24 citation statements)

References 34 publications

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“…The idea behind this method is quite simple: a MSD curve (i.e., an average square displacement as a function of the time lag) is quantified from a single experimental trajectory and then fitted with a theoretical expression [ 18 ]. A linear best fit indicates normal diffusion (Brownian motion) [ 19 ], which corresponds to a particle moving freely in its environment. Such a particle neither interacts with other distant particles nor is hindered by any obstacles.…”

Section: Introductionmentioning

confidence: 99%

Impact of Feature Choice on Machine Learning Classification of Fractional Anomalous Diffusion

Loch-Olszewska

Szwabiński

2020

Entropy

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The growing interest in machine learning methods has raised the need for a careful study of their application to the experimental single-particle tracking data. In this paper, we present the differences in the classification of the fractional anomalous diffusion trajectories that arise from the selection of the features used in random forest and gradient boosting algorithms. Comparing two recently used sets of human-engineered attributes with a new one, which was tailor-made for the problem, we show the importance of a thoughtful choice of the features and parameters. We also analyse the influence of alterations of synthetic training data set on the classification results. The trained classifiers are tested on real trajectories of G proteins and their receptors on a plasma membrane.

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Section: Introductionmentioning

confidence: 99%

Impact of Feature Choice on Machine Learning Classification of Fractional Anomalous Diffusion

Loch-Olszewska

Szwabiński

2020

Entropy

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“…[46,47] In many other diffusion-controlled systems where the above conditions are not met, significant deviations have been observed, leading to an anomalous transport behavior. [45,48] Anomalous dynamics is ubiquitous in soft condensed matter, and has been reported in a wide variety of systems, [47,49] including hydrogels. [50,51] Lèvy flights models [52][53][54] have attracted a considerable deal of interest, due to their ability to describe a number of anomalous superdiffusive phenomena (see below).…”

Section: Introductionmentioning

confidence: 99%

Evidence of superdiffusive nanoscale motion in anionic polymeric hydrogels: Analysis of PGSE- NMR data and comparison with drug release properties

Castiglione

Casalegno

Ferro

et al. 2019

Journal of Controlled Release

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Polymeric hydrogels are promising candidates for drug delivery applications, thanks to their ability to encapsulate, transport and release a wide range of chemicals. The successful application of these materials requires a deep understanding of the mechanisms governing solute transport at the nanoscale and its impact on release kinetics. In this work, we investigate the translational diffusion of ibuprofen loaded in anionic agarose-carbomer (AC) hydrogels by 1 H high resolution magic angle spinning (HR-MAS) NMR spectroscopy, and compare it to its macroscopic release kinetics. The analysis of the experimental NMR data provides the first evidence of superdiffusion for ibuprofen in AC hydrogels. Superdiffusive transport is observed in the majority of our samples, especially those with the smallest mesh size (7 nm) and highest ibuprofen concentrations (90-120 mg/mL). This outcome is rationalized in terms of heavy-tailed distributions of spatial displacements (Lèvy flights) and of waiting times, which depend on the nanoscopic structural heterogeneity of the gels and the strong but reversible association between ibuprofen and the agarose matrix.

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“…The value of the latter one is used to discriminate between different diffusion types. The case

corresponds to the normal diffusion (ND), also known as the Brownian motion [ 5 ]. In this physical scenario, a particle moves freely in its environment.…”

Section: Models and Methodsmentioning

confidence: 99%

“…However, following Refs. [ 43 , 44 ], we decided to consider four models: normal diffusion [ 5 ], directed motion (DM) [ 22 , 66 , 67 ], fractional Brownian motion (FBM) in subdiffusive mode [ 68 ], and confined diffusion (CD) [ 40 ]. According to Saxton [ 7 ], for those basic models of diffusion in 2D, we have:

Here, v is the drift velocity in the directed motion, the constants

and

characterize the shape of the confinement, and

is the confinement radius.…”

Section: Models and Methodsmentioning

confidence: 99%

“…The data collected in SPT experiments often reveal deviations from the Brownian motion [ 5 ], i.e., the normal diffusion governed by the Fick’s laws [ 6 ] and characterized by a linear time-dependence of the mean square displacement (MSD) of the molecules. Those deviations are referred to as anomalous diffusion, a field intensively studied in the physical community [ 7 , 8 , 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

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Detection of Anomalous Diffusion with Deep Residual Networks

Gajowczyk

Szwabiński

2021

Entropy

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Identification of the diffusion type of molecules in living cells is crucial to deduct their driving forces and hence to get insight into the characteristics of the cells. In this paper, deep residual networks have been used to classify the trajectories of molecules. We started from the well known ResNet architecture, developed for image classification, and carried out a series of numerical experiments to adapt it to detection of diffusion modes. We managed to find a model that has a better accuracy than the initial network, but contains only a small fraction of its parameters. The reduced size significantly shortened the training time of the model. Moreover, the resulting network has less tendency to overfitting and generalizes better to unseen data.

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Characterization of diffusion processes: Normal and anomalous regimes

Cited by 38 publications

References 34 publications

Impact of Feature Choice on Machine Learning Classification of Fractional Anomalous Diffusion

Impact of Feature Choice on Machine Learning Classification of Fractional Anomalous Diffusion

Evidence of superdiffusive nanoscale motion in anionic polymeric hydrogels: Analysis of PGSE- NMR data and comparison with drug release properties

Detection of Anomalous Diffusion with Deep Residual Networks

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