Related papers: Objective comparison of methods to decode anomalou…
Streaming anomaly detection refers to the problem of detecting anomalous data samples in streams of data. This problem poses challenges that classical and deep anomaly detection methods are not designed to cope with, such as conceptual…
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…
The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light…
Brownian motion is essential for describing diffusion in systems ranging from simple to complex liquids. Unlike simple liquids, which consist of only a solvent, complex liquids, such as colloidal suspensions or the cytoplasm of a cell, are…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
Improving the reliability of deployed machine learning systems often involves developing methods to detect out-of-distribution (OOD) inputs. However, existing research often narrowly focuses on samples from classes that are absent from the…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Distance-based methods involve the computation of distance values between features and are a well-established paradigm in machine learning. In anomaly detection, anomalies are identified by their large distance from normal data points.…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
Anomaly detection is a challenging task that frequently arises in practically all areas of industry and science, from fraud detection and data quality monitoring to finding rare cases of diseases and searching for new physics. Most of the…
Solid-state ionic conduction is a key enabler of electrochemical energy storage and conversion. The mechanistic connections between material processing, defect chemistry, transport dynamics, and practical performance are of considerable…
The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
We propose two nonlinear random walk models which are suitable for the analysis of both chemotaxis and anomalous transport. We derive the balance equations for the population density for the case when the transition rate for a random walk…
Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in…
We show that multichannel quantum systems with uncorrelated but asymmetric Anderson-type disorder can exhibit anomalous diffusion, even in the absence of heavy-tailed disorder. Using a minimal two-channel model with channel asymmetry, we…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
Recent advancements in diffusion models have demonstrated significant success in unsupervised anomaly segmentation. For anomaly segmentation, these models are first trained on normal data; then, an anomalous image is noised to an…