Related papers: Objective comparison of methods to decode anomalou…
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…
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…
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…
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…
Anomaly detection, the technique of identifying abnormal samples using only normal samples, has attracted widespread interest in industry. Existing one-model-per-category methods often struggle with limited generalization capabilities due…
Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation…
While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at…
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…
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…
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…
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent…
In this work animations of the random walk movement using a freeware Algodoo were done in order to support teaching the concepts of Brownian Motion. The random walk movement were simulate considering elastic collision between the particles…
In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion, and precisely characterize its nature and parameters. Often, this task is strongly impacted by data…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
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…
Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement…
We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a…
The presence of concept drift poses challenges for anomaly detection in time series. While anomalies are caused by undesirable changes in the data, differentiating abnormal changes from varying normal behaviours is difficult due to…
The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…