Related papers: AnDi: The Anomalous Diffusion Challenge
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and…
Early detection of anomalies in medical images such as brain MRI is highly relevant for diagnosis and treatment of many conditions. Supervised machine learning methods are limited to a small number of pathologies where there is good…
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 models (DMs) have emerged as a powerful class of generative AI models, showing remarkable potential in anomaly detection (AD) tasks across various domains, such as cybersecurity, fraud detection, healthcare, and manufacturing. The…
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
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…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A…
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…
When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled…
Anomaly detection is the process of identifying atypical data samples that significantly deviate from the majority of the dataset. In the realm of clinical screening and diagnosis, detecting abnormalities in medical images holds great…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…