Related papers: Measurement of Anomalous Diffusion Using Recurrent…
The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are…
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…
Time series anomaly detection plays a critical role in automated monitoring systems. Most previous deep learning efforts related to time series anomaly detection were based on recurrent neural networks (RNN). In this paper, we propose 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.…
The superdiffusion behavior, i.e. $<x^2(t)> \sim t^{2 \nu}$, with $\nu > 1/2$, in general is not completely characherized by a unique exponent. We study some systems exhibiting strong anomalous diffusion, i.e. $<|x(t)|^q> \sim t^{q \nu(q)}$…
Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and…
Anomaly detection has garnered extensive applications in real industrial manufacturing due to its remarkable effectiveness and efficiency. However, previous generative-based models have been limited by suboptimal reconstruction quality,…
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
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…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
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…
Anomalous diffusion processes pose a unique challenge in classification and characterization. Previously (Mangalam et al., 2023, Physical Review Research 5, 023144), we established a framework for understanding anomalous diffusion using…
Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…
This paper investigates the performance of diffusion models for video anomaly detection (VAD) within the most challenging but also the most operational scenario in which the data annotations are not used. As being sparse, diverse,…
Understanding and identifying different types of single molecules' diffusion that occur in a broad range of systems (including living matter) is extremely important, as it can provide information on the physical and chemical characteristics…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
Unsupervised Anomalous Sound Detection (ASD) aims to design a generalizable method that can be used to detect anomalies when only normal sounds are given. In this paper, Anomalous Sound Detection based on Diffusion Models (ASD-Diffusion) is…
Real-time lightweight time series anomaly detection has become increasingly crucial in cybersecurity and many other domains. Its ability to adapt to unforeseen pattern changes and swiftly identify anomalies enables prompt responses and…
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…