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The high performance of denoising diffusion models for image generation has paved the way for their application in unsupervised medical anomaly detection. As diffusion-based methods require a lot of GPU memory and have long sampling times,…
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…
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…
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…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
Generative models have demonstrated significant success in anomaly detection and segmentation over the past decade. Recently, diffusion models have emerged as a powerful alternative, outperforming previous approaches such as GANs and VAEs.…
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…
We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes…
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…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…
Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied…
The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to…
The random propagation of molecules in a fluid medium is characterized by the spontaneous diffusion law as well as the interaction between the environment and molecules. In this paper, we embody the anomalous diffusion theory for modeling…
The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
Graph anomaly detection (GAD) aims to identify nodes or substructures whose behavior or attributes deviate significantly from the overall pattern in graph-structured data, with critical applications in financial risk control, social network…
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…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a…
Anomaly detection (AD) plays a pivotal role across diverse domains, including cybersecurity, finance, healthcare, and industrial manufacturing, by identifying unexpected patterns that deviate from established norms in real-world data.…