Bayesian deep learning for error estimation in the analysis of anomalous diffusion

Nature Communications, Journal Year: 2022, Volume and Issue: 13(1)

Published: Nov. 7, 2022

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety systems, from single-molecule living-cells to movement ecology. The quest is decipher the physical mechanisms encoded data and thus better understand probed systems. We here augment recently proposed machine-learning for decoding anomalous-diffusion include an uncertainty estimate addition predicted output. To avoid Black-Box-Problem Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian used train models both classification diffusion model regression anomalous exponent single-particle-trajectories. Evaluating their performance, we find that these can achieve well-calibrated error while maintaining high prediction accuracies. In analysis output predictions relate properties underlying models, providing insights into learning process machine relevance

Language: Английский

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Towards a robust criterion of anomalous diffusion

Communications Physics, Journal Year: 2022, Volume and Issue: 5(1)

Published: Nov. 28, 2022

Abstract Anomalous-diffusion, the departure of spreading dynamics diffusing particles from traditional law Brownian-motion, is a signature feature large number complex soft-matter and biological systems. Anomalous-diffusion emerges due to variety physical mechanisms, e.g., trapping interactions or viscoelasticity environment. However, sometimes systems are erroneously claimed be anomalous, despite fact that true motion Brownian—or vice versa. This ambiguity in establishing whether as normal anomalous can have far-reaching consequences, predictions for reaction- relaxation-laws. Demonstrating system exhibits normal- anomalous-diffusion highly desirable vast host applications. Here, we present criterion based on method power-spectral analysis single trajectories. The robustness this studied trajectories fractional-Brownian-motion, ubiquitous stochastic process description anomalous-diffusion, presence two types measurement errors. In particular, find our very robust subdiffusion. Various tests surrogate data absence additional positional noise demonstrate efficacy practical contexts. Finally, provide proof-of-concept diverse experiments exhibiting both anomalous-diffusion.

Language: Английский

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Anomalous diffusion, nonergodicity, non-Gaussianity, and aging of fractional Brownian motion with nonlinear clocks

Physical review. E, Journal Year: 2023, Volume and Issue: 108(3)

Published: Sept. 13, 2023

How do nonlinear clocks in time and/or space affect the fundamental properties of a stochastic process? Specifically, how precisely may ergodic processes such as fractional Brownian motion (FBM) acquire predictable nonergodic and aging features being subjected to conditions? We address these questions current study. To describe different types non-Brownian particles-including power-law anomalous, ultraslow or logarithmic, well superfast exponential diffusion-we here develop analyze generalized process scaled-fractional (SFBM). The time- space-SFBM are, respectively, constructed based on FBM running with clocks. statistical characteristics non-Gaussianity particle displacements, nonergodicity, are quantified for by selecting latter parametrize ultraslow, diffusion. results our computer simulations fully consistent analytical predictions several functional forms thoroughly examine behaviors probability-density function, mean-squared displacement, time-averaged factor. Our applicable rationalizing impact superimposed onto FBM-type dynamics. SFBM offers general framework universal more precise model-based description nonergodic, non-Gaussian, diffusion single-molecule-tracking observations.

Language: Английский

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Fractional Langevin equation far from equilibrium: Riemann-Liouville fractional Brownian motion, spurious nonergodicity, and aging

Physical review. E, Journal Year: 2025, Volume and Issue: 111(1)

Published: Jan. 13, 2025

We consider the fractional Langevin equation far from equilibrium (FLEFE) to describe stochastic dynamics which do not obey fluctuation-dissipation theorem, unlike conventional (FLE). The solution of this is Riemann-Liouville Brownian motion (RL-FBM), also known in literature as FBM II. Spurious nonergodicity, stationarity, and aging properties are explored for all admissible values α>1/2 order α time-fractional Caputo derivative FLEFE. increments process asymptotically stationary. However when 1/2<α<3/2, time-averaged mean-squared displacement (TAMSD) does converge (MSD). Instead, it converges increment (MSI) or structure function, leading phenomenon spurious nonergodicity. When α≥3/2, FLEFE nonergodic, however higher ergodic. discuss effect by investigating influence an time t_{a} on MSD, TAMSD autocovariance function increments. find that under strong conditions becomes ergodic, become stationary domain 1/2<α<3/2.

Language: Английский

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Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories

The Journal of Physical Chemistry Letters, Journal Year: 2023, Volume and Issue: 14(35), P. 7910 - 7923

Published: Aug. 30, 2023

Single-particle traces of the diffusive motion molecules, cells, or animals are by now routinely measured, similar to stochastic records stock prices weather data. Deciphering mechanism behind recorded dynamics is vital in understanding observed systems. Typically, task decipher exact type diffusion and/or determine system parameters. The tools used this endeavor currently being revolutionized modern machine-learning techniques. In Perspective we provide an overview recently introduced methods for time series, most notably, those successfully competing anomalous challenge. As such often criticized their lack interpretability, focus on means include uncertainty estimates and feature-based approaches, both improving interpretability providing concrete insight into learning process machine. We expand discussion examining predictions different out-of-distribution also comment expected future developments.

Language: Английский

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Directedeness, correlations, and daily cycles in springbok motion: From data via stochastic models to movement prediction

Physical Review Research, Journal Year: 2023, Volume and Issue: 5(4)

Published: Nov. 7, 2023

How predictable is the next move of an animal? Specifically, which factors govern short- and long-term motion patterns overall dynamics land-bound, plant-eating animals in general ruminants particular? To answer this question, we here study movement springbok antelopes Antidorcas marsupialis. We propose several complementary statistical-analysis techniques combined with machine-learning approaches to analyze---across multiple time scales---the recorded GPS tracking collared springboks at a private wildlife reserve Namibia. As result, are able predict within hour certainty about 20%. The remaining 80% stochastic nature induced by unaccounted modeling algorithm individual behavioral features springboks. find that directedness contributes approximately 17% predicted fraction. measure for directedeness strongly dependent on daily cycle activity. previously known affinity their water points, as from our algorithm, accounts only 3% deterministic component motion. Moreover, resting points found affect least much formally studied effects points. generality these statements underlying reasons other can be examined basis tools future.

Language: Английский

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Characterization of anomalous diffusion through convolutional transformers

Journal of Physics A Mathematical and Theoretical, Journal Year: 2023, Volume and Issue: 56(1), P. 014001 - 014001

Published: Jan. 3, 2023

Abstract The results of the Anomalous Diffusion Challenge (AnDi Challenge) (Muñoz-Gil G et al 2021 Nat. Commun. 12 6253) have shown that machine learning methods can outperform classical statistical methodology at characterization anomalous diffusion in both inference exponent α associated with each trajectory (Task 1), and determination underlying diffusive regime which produced such trajectories 2). Furthermore, five teams finished top three across tasks AnDi Challenge, those used recurrent neural networks (RNNs). While RNNs, like long short-term memory network, are effective long-term dependencies sequential data, their key disadvantage is they must be trained sequentially. In order to facilitate training larger data sets, by parallel, we propose a new transformer based network architecture for diffusion. Our architecture, Convolutional Transformer (ConvTransformer) uses bi-layered convolutional extract features from our thought as being words sentence. These then fed two encoding blocks perform either regression 1 1D) or classification 2 1D). To knowledge, this first time transformers been characterizing Moreover, may block has without need decoding positional encoding. Apart able train show ConvTransformer previous state art determining short (length 10–50 steps), most important experimental researchers.

Language: Английский

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Time-dependent probability density function for partial resetting dynamics

New Journal of Physics, Journal Year: 2023, Volume and Issue: 25(8), P. 082002 - 082002

Published: Aug. 1, 2023

Abstract Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes occasional reset diffusing particle to its starting point effects, inter alia, optimal first-passage times target. Recently concept partial resetting, which given fraction current value process, has been established associated search behaviour analysed. Here we go one step further develop general technique determine time-dependent probability density function (PDF) for Markov with resetting. We obtain an exact representation PDF case symmetric Lévy flights stable index 0 < α ⩽ 2 . For Cauchy Brownian motions (i.e. $\alpha = 1,2$?> = 1 , ), this can be expressed terms elementary functions position space. also stationary PDF. Our numerical analysis demonstrates intricate crossover behaviours as time.

Language: Английский

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Memory-multi-fractional Brownian motion with continuous correlations

Physical Review Research, Journal Year: 2023, Volume and Issue: 5(3)

Published: Aug. 23, 2023

We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent α(t) in changing environment. In MMFBM built-in, long-range is continuously modulated by α(t). derive essential statistical properties such as its response function, mean-squared displacement (MSD), autocovariance and Gaussian distribution. contrast existing forms FBM time-varying exponents but reset structure, instantaneous dynamic influenced process history, e.g., we show that after steplike change scaling MSD α step may be determined value before change. versatile useful for correlated physical systems nonequilibrium initial conditions environment.Received 9 October 2022Accepted 14 July 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L032025Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasAnomalous diffusionFractional motionIntracellular transportInterdisciplinary PhysicsBiological PhysicsStatistical Physics

Language: Английский

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Semantic segmentation of anomalous diffusion using deep convolutional networks

Physical Review Research, Journal Year: 2024, Volume and Issue: 6(1)

Published: Jan. 16, 2024

Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes states, we propose a deep learning model (U-AnDi) for the semantic segmentation trajectories. This is developed dilated causal convolution (DCC), gated activation unit (GAU), and U-Net architecture. The study addresses two key subtasks related trajectory changepoint detection, concentrating on variations exponents dynamic models. Additionally, extended analyses are conducted single-model trajectories, multistate biological added correlation functions. By rationally designing comparative models evaluating performance U-AnDi against models, discover that consistently outperforms other across all tasks, thereby affirming its superiority field. edge also sheds light interpretability U-AnDi's core components: DCC, GAU, U-Net. clarity which components contribute success underscores their congruence intrinsic physics underlying diffusion. Furthermore, our examined real-world data: transmembrane proteins cell membrane surfaces, results highly consistent experimental observations. Our findings could offer heuristic solution detection heterogeneous single-molecule/particle tracking experiments, have potential be generalized as universal scheme time-series segmentation.

Language: Английский

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