Related papers: Characterization of anomalous diffusion classical …

Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of…

Anomaly detection aims to identify samples that deviate from the nominal data distribution and is central to many safety-critical applications. However, developing effective anomaly detection methods for categorical, mixed-type, 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…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

Anomalies represent rare observations (e.g., data records or events) that deviate significantly from others. Over several decades, research on anomaly mining has received increasing interests due to the implications of these occurrences in…

Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…

Reconstruction-based approaches have achieved remarkable outcomes in anomaly detection. The exceptional image reconstruction capabilities of recently popular diffusion models have sparked research efforts to utilize them for enhanced…

Accurate pedestrian trajectory prediction is crucial for ensuring safety and efficiency in autonomous driving and human-robot interaction scenarios. Earlier studies primarily utilized sufficient observational data to predict future…

Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…

Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto…

Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes undergoing in a range of materials including living cells and tissues. However, extracting that information is not a…

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…

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…

Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…

It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on "intermediate" time scales before diffusion sets in.…

Diffusion models are rapidly redefining 3D anomaly detection in point cloud data. As 3D sensing becomes integral to modern manufacturing, reliable anomaly detection is essential for high-throughput quality assurance and process control. Yet…

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…

Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…

Anomaly detection is an emerging approach in digital pathology for its ability to efficiently and effectively utilize data for disease diagnosis. While supervised learning approaches deliver high accuracy, they rely on extensively annotated…

Anomaly detection is a complex problem due to the ambiguity in defining anomalies, the diversity of anomaly types (e.g., local and global defect), and the scarcity of training data. As such, it necessitates a comprehensive model capable of…