Related papers: Measurement of Anomalous Diffusion Using Recurrent…
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 investigate the occurrence of anomalous diffusive transport associated with acoustic wave fields propagating through highly-scattering periodic media. Previous studies had correlated the occurrence of anomalous diffusion to either the…
The introduction of diffusion models in anomaly detection has paved the way for more effective and accurate image reconstruction in pathologies. However, the current limitations in controlling noise granularity hinder diffusion models'…
We revisit the diffusion properties and the mean drift induced by an external field of a random walk process in a class of branched structures, as the comb lattice and the linear chains of plaquettes. A simple treatment based on scaling…
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights…
Anomaly detection in medical imaging is a challenging task in contexts where abnormalities are not annotated. This problem can be addressed through unsupervised anomaly detection (UAD) methods, which identify features that do not match with…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
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 phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
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 $1-p$…
Industrial defect detection systems face critical limitations when confined to one-class anomaly detection paradigms, which assume uniform outlier distributions and struggle with data scarcity in real-world manufacturing environments. We…
In order to detect unknown intrusions and runtime errors of computer programs, the cyber-security community has developed various detection techniques. Anomaly detection is an approach that is designed to profile the normal runtime behavior…
Existing image SR and generic diffusion models transfer poorly to fluid SR: they are sampling-intensive, ignore physical constraints, and often yield spectral mismatch and spurious divergence. We address fluid super-resolution (SR) with…
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…
Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
We propose a physics-informed anomaly detection framework for collider data based on a Bayesian latent diffusion model. Our method combines a probabilistic encoder with diffusion dynamics in the latent space, allowing for stable and…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here, a novel method to elucidate the fluctuating diffusivity from trajectory data is developed. The time-averaged…