Fractional Differential Equations Solutions

AnDi-J: diffusion analysis of single-particle tracking data in Fiji

AnDi-J is a Fiji plugin that analyzes single-particle tracking data using classical and machine learning methods to extract diffusion properties and classify trajectories.

Anisotropic subdiffusion in the cytoplasm of living cells

This study tracks peroxisomes in living cells to show the cytoplasm has a nematic-like sub-structure with directional motion, even without cytoskeletal filaments or ER.

Extracting anomalous diffusion parameters from multi-state ensembles of short single molecule trajectories.

The paper evaluates analysis methods for extracting diffusion parameters from single-molecule trajectories and shows that single-track analysis outperforms bulk methods.

FreeTrace enables fractional Brownian motion-based single-molecule tracking and robust anomalous diffusion analysis

Practical considerations for accurate estimation of diffusion parameters from single-particle tracking in living cells

This study provides strategies to improve diffusion parameter estimation in single-particle tracking by optimizing exposure time, sampling rate, and nonlinear MSD fitting.

Hierarchical Heterogeneities in Spatiotemporal Dynamics of the Cytoplasm

This study uses differential dynamic microscopy to analyze cytoplasmic dynamics in Xenopus laevis egg extracts and HeLa cells, revealing subdiffusive motion and cytoskeletal influences on fluidity.

Fractional Calculus in Epigenetics

This paper introduces a fractional calculus framework to model DNA methylation dynamics, showing improved fit compared to standard exponential models.

Extended fractional-polynomial generalizations of diffusion and Fisher-KPP equations on directed networks: Modeling neurodegenerative progression

The paper generalizes diffusion and Fisher-KPP equations on networks to model neurodegenerative progression, accounting for anomalous diffusion in brain structures.

Chromatin phase separated nanoregions regulated by cross-linkers and explored by single particle trajectories

The paper studies how cross-linkers generate chromatin phase separated nanoregions and quantifies their impact on molecular access using single particle trajectories.

MPTHub: an open-source software for characterizing the transport of particles in biorelevant media

MPTHub is a software tool for analyzing particle trajectories in biorelevant media, providing rapid and reliable computation of transport parameters.