Super-Resolved Anomalous Diffusion: Deciphering the Joint Distribution of Anomalous Exponent and Diffusion...

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Anomalous diffusion describes molecular motion in heterogeneous media using mean-squared displacement.
• Experimental studies report populations of anomalous diffusion parameters (α and D), leading to observed variability.
• Distinguishing true parameter populations from finite-duration recording artifacts is crucial for accurate interpretation.

Purpose of the Study:

• To disentangle the contributions of parameter populations and finite-duration recordings to anomalous diffusion variability.
• To introduce and analyze novel estimators for anomalous diffusion parameters.
• To provide a theoretical framework and practical guidelines for analyzing experimental data.

Main Methods:

• Development of estimators based on time-averaged mean-squared displacement.
• Application of a copula approach to derive the joint density function of parameter estimations.
• Comparison with numerical simulations of fractional Brownian motion.
• Quantification of accuracy using Hellinger distance.

Main Results:

• A universal methodology applicable to Gaussian processes and quadratic time-averaged statistics was introduced.
• A formula for the joint density function of estimated anomalous diffusion parameters was derived.
• The experimentally observed relation D∝exp(αc_{1}+c_{2}) was theoretically explained with an exact expression.
• Numerical simulations validated the theoretical findings and accuracy.

Conclusions:

• The developed methodology effectively distinguishes between true parameter populations and finite-duration recording effects in anomalous diffusion.
• The study provides a theoretical basis for understanding the relationship between anomalous diffusion parameters.
• Practical guidelines and routines are offered for fitting experimental data, enhancing the analysis of molecular motion in complex systems.