Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking

Lavrynenko, Roman; Kirichenko, Lyudmyla; Yakovlev, Sergiy; Lavrynenko, Sophia; Ryabova, Nataliya

doi:10.3390/app15148000

Open AccessArticle

Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking

by

Roman Lavrynenko

¹

,

Lyudmyla Kirichenko

^2,3

,

Sergiy Yakovlev

^2,3,*

,

Sophia Lavrynenko

¹

and

Nataliya Ryabova

¹

Artificial Intelligence Department, Kharkiv National University of Radio Electronics, 61166 Kharkiv, Ukraine

²

Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland

³

Institute of Computer Science and Artificial Intelligence, V.N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine

^*

Author to whom correspondence should be addressed.

Appl. Sci. 2025, 15(14), 8000; https://doi.org/10.3390/app15148000

Submission received: 16 June 2025 / Revised: 12 July 2025 / Accepted: 16 July 2025 / Published: 18 July 2025

(This article belongs to the Section Applied Biosciences and Bioengineering)

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Abstract

The analysis of anomalous diffusion characteristics within single-particle tracking data is a key problem in several applied-science domains, including biosignal processing, bioinformatics, and biotechnology. This task becomes particularly challenging in the presence of short trajectories, localization errors, and non-ergodicity, features that are common in real experimental data. To address these limitations, this work proposes an approach that improves the robustness and accuracy of estimating the anomalous diffusion exponent α, even for very short trajectories of up to 10 points. The approach includes an ensemble-based variance estimation of the exponent α, along with a bias correction based on time–ensemble averaged mean squared displacement, which reduces the systematic bias. These components integrate well into neural network architectures and are suitable for analyzing experimental trajectories in biotechnology and bioprocess engineering applications.

Keywords: AnDi challenge; anomalous diffusion; anomalous diffusion exponent; Hurst exponent; single-particle tracking; TA-MSD

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MDPI and ACS Style

Lavrynenko, R.; Kirichenko, L.; Yakovlev, S.; Lavrynenko, S.; Ryabova, N. Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking. Appl. Sci. 2025, 15, 8000. https://doi.org/10.3390/app15148000

AMA Style

Lavrynenko R, Kirichenko L, Yakovlev S, Lavrynenko S, Ryabova N. Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking. Applied Sciences. 2025; 15(14):8000. https://doi.org/10.3390/app15148000

Chicago/Turabian Style

Lavrynenko, Roman, Lyudmyla Kirichenko, Sergiy Yakovlev, Sophia Lavrynenko, and Nataliya Ryabova. 2025. "Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking" Applied Sciences 15, no. 14: 8000. https://doi.org/10.3390/app15148000

APA Style

Lavrynenko, R., Kirichenko, L., Yakovlev, S., Lavrynenko, S., & Ryabova, N. (2025). Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking. Applied Sciences, 15(14), 8000. https://doi.org/10.3390/app15148000

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Ensemble-Based Correction for Anomalous Diffusion Exponent Estimation in Single-Particle Tracking

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