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The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
Fluorescence Correlation Spectroscopy (FCS) is a powerful single-molecule technique which allows for measuring motion (diffusion, flow), concentration, and molecular interaction kinetics of fluorescent molecules from picomolar to micromolar…
Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating…
Understanding and identifying different types of single molecules' diffusion that occur in a broad range of systems (including living matter) is extremely important, as it can provide information on the physical and chemical characteristics…
Anomaly detection is a fundamental task in machine learning and data mining, with significant applications in cybersecurity, industrial fault diagnosis, and clinical disease monitoring. Traditional methods, such as statistical modeling and…
Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…
Conformational dynamics of biomolecules are of fundamental importance for their function. Single-molecule F\"orster Resonance Energy Transfer (smFRET) is a powerful approach to inform on the structure and the dynamics of labeled molecules.…
Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from…
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…
The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are…
Scanning fluorescence correlation spectroscopy (SFCS) with a scan path perpendicular to the membrane plane was introduced to measure diffusion and interactions of fluorescent components in free standing biomembranes. Using a confocal laser…
Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the…
Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
Countless systems in biology, physics, and finance undergo diffusive dynamics. Many of these systems, including biomolecules inside cells, active matter systems and foraging animals, exhibit anomalous dynamics where the growth of the mean…
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The diffusion of macromolecules in cells and in complex fluids is often found to deviate from simple Fickian diffusion. One explanation offered for this behavior is that molecular crowding renders diffusion anomalous, where the mean-squared…