A guide to single-particle tracking

Nature Reviews Methods Primers, Journal Year: 2024, Volume and Issue: 4(1)

Published: Sept. 12, 2024

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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Enhancing daily reference evapotranspiration (ETref) prediction across diverse climatic zones: A pattern mining approach with DIRECTORS model

Journal of Hydrology, Journal Year: 2025, Volume and Issue: unknown, P. 133045 - 133045

Published: March 1, 2025

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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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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Time scales in the dynamics of political opinions and the voter model

New Journal of Physics, Journal Year: 2024, Volume and Issue: 26(2), P. 023040 - 023040

Published: Feb. 1, 2024

Abstract Opinions in human societies are measured by political polls on time scales of months to years. Such opinion do not resolve the effects individual interactions but constitute a stochastic process. Voter models with zealots (individuals who change their opinions) can describe mean-field dynamics systems where no consensus is reached. We show that for large populations, voter model equivalent noisy and it has single characteristic scale associated number population. discuss which parameters observable real data analysing series approval ratings several leaders match statistical behaviour using technique time-averaged mean squared displacement. The opinions around 12 months, so cannot be resolved election data, resolution effective population size all fitted sets much smaller than size, indicates positive correlations successive steps. also heterogeneity voters as cause subdiffusion long scales, i.e. slow changes society.

Language: Английский

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Multifractal spectral features enhance classification of anomalous diffusion

Physical review. E, Journal Year: 2024, Volume and Issue: 109(4)

Published: April 15, 2024

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)], we established comprehensive framework for understanding anomalous using multifractal formalism. The present delves into potential spectral features effectively distinguishing trajectories from five widely used models: fractional Brownian motion, scaled continuous-time random walk, annealed transient time L\'evy walk. We generate extensive datasets comprising ${10}^{6}$ these models extract multiple spectra each trajectory to accomplish this. Our investigation entails thorough analysis neural network performance, encompassing derived varying numbers spectra. also explore integration traditional feature datasets, enabling us assess impact comprehensively. To ensure statistically meaningful comparison, categorize concept groups train networks designated group. Notably, several demonstrate similar levels accuracy, with highest performance observed utilizing moving-window characteristics $p$ varation features. Multifractal features, particularly those three involving different timescales cutoffs, closely follow, highlighting robust discriminatory potential. Remarkably, exclusively trained on single spectrum exhibits commendable surpassing other groups. summary, our findings underscore diverse potent efficacy enhancing predictive capacity machine learning classify processes.

Language: Английский

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Modelling intermittent anomalous diffusion with switching fractional Brownian motion

New Journal of Physics, Journal Year: 2023, Volume and Issue: 25(10), P. 103031 - 103031

Published: Oct. 1, 2023

Abstract The stochastic trajectories of molecules in living cells, as well the dynamics many other complex systems, often exhibit memory their path over long periods time. In addition, these systems can show dynamic heterogeneities due to which motion changes along trajectories. Such effects manifest themselves spatiotemporal correlations. Despite broad occurrence heterogeneous nature, analysis is still quite poorly understood and tools model them are largely missing. We contribute tackling this problem by employing an integral representation Mandelbrot’s fractional Brownian that compliant with varying parameters while maintaining memory. Two types switching analysed, transitions arising from a Markovian process scale-free intermittent processes. obtain simple formulas for classical statistics processes, namely mean squared displacement power spectral density. Further, method identify based on distribution displacements described. A validation given experimental measurements quantum dots cytoplasm live mammalian cells were obtained single-particle tracking.

Language: Английский

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Distinguishing between fractional Brownian motion with random and constant Hurst exponent using sample autocovariance-based statistics

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(4)

Published: April 1, 2024

Fractional Brownian motion (FBM) is a canonical model for describing dynamics in various complex systems. It characterized by the Hurst exponent, which responsible correlation between FBM increments, its self-similarity property, and anomalous diffusion behavior. However, recent research indicates that classical may be insufficient experimental observations when exponent varies from trajectory to trajectory. As result, modifications of have been considered literature, with natural extension being random exponent. In this paper, we discuss problem distinguishing two models: (i) constant (ii) analyzing probabilistic properties statistics represented quadratic forms. These recently found application Gaussian processes proven serve as efficient tools hypothesis testing. Here, examine statistics-the sample autocovariance function empirical anomaly measure-utilizing models. Based on these statistics, introduce testing procedure differentiate We present analytical simulation results considering two-point beta distributions exemplary Finally, demonstrate utility presented methodology, analyze real-world datasets financial market single particle tracking experiment biological gels.

Language: Английский

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Regular and anomalous diffusion: I. Foundations

Journal of Physics A Mathematical and Theoretical, Journal Year: 2024, Volume and Issue: 57(23), P. 233002 - 233002

Published: May 14, 2024

Abstract Diffusion is a generic term for random motions whose positions become more and diffuse with time. of major importance in numerous areas science engineering, the research diffusion vast profound. This paper first stochastic ‘intro series’ to multidisciplinary field diffusion. The sets off from basic question: how quantitatively measure diffusivity? Having answered question, carries on follow-up question regarding statistical behaviors diffusion: what further knowledge can diffusivity provide, when it do so? answers lead an assortment notions topics including: persistence anti-persistence; aging anti-aging; short-range long-range dependence; Wiener–Khinchin theorem its generalizations; spectral densities, white noise, their colored noises. Observing macro level, culminates with: universal emergence power-law diffusivity; three regimes—one regular, two anomalous; 1/f noise. entirely self-contained, prerequisites are undergraduate mathematics statistics.

Language: Английский

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