Related papers: Objective comparison of methods to decode anomalou…

Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous…

The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…

Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. In this paper, we compute analytically the diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map.…

We study the 2D motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the…

Anomaly detection is an important problem that has been well-studied within diverse research areas and application domains. The aim of this survey is two-fold, firstly we present a structured and comprehensive overview of research methods…

A random walk scheme, consisting of alternating phases of regular Brownian motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and…

Deep learning-based methods have achieved a breakthrough in image anomaly detection, but their complexity introduces a considerable challenge to understanding why an instance is predicted to be anomalous. We introduce a novel explanation…

Advection-diffusion equations describe a large family of natural transport processes, e.g., fluid flow, heat transfer, and wind transport. They are also used for optical flow and perfusion imaging computations. We develop a machine learning…

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong…

In this paper, we study the competition of two diffusion processes for achieving the maximum possible diffusion in an area. This competition, however, does not occur in the same circumstance; one of these processes is a normal diffusion…

Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…

We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$…

In this paper we investigate the behavior of particles crossing a neat interface between two media. A Monte Carlo and analytical model, based on fractional derivatives, are presented and discussed in detail, together with a comparison.…

Anomaly inspection plays an important role in industrial manufacture. Existing anomaly inspection methods are limited in their performance due to insufficient anomaly data. Although anomaly generation methods have been proposed to augment…

In the anomaly detection field, the scarcity of anomalous samples has directed the current research emphasis towards unsupervised anomaly detection. While these unsupervised anomaly detection methods offer convenience, they also overlook…

The onset of the Rayleigh-Benard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion…

The Mean Square Displacement is a central tool in the analysis of Single Particle Tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time-averages on single particle…

Multivariate time-series anomaly detection, which is critical for identifying unexpected events, has been explored in the field of machine learning for several decades. However, directly applying these methods to data from forceful tool use…

Anomaly detection in complex, high-dimensional data, such as UAV sensor readings, is essential for operational safety but challenging for existing methods due to their limited sensitivity, scalability, and inability to capture intricate…