Related papers: Multifractal-spectral features enhance classificat…
Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated…
Several techniques for multivariate time series anomaly detection have been proposed recently, but a systematic comparison on a common set of datasets and metrics is lacking. This paper presents a systematic and comprehensive evaluation of…
We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are…
In recent years, research and development in nanoscale science and technology have grown significantly, with electrical transport playing a key role. A natural challenge for its description is to shed light on anomalous behaviours observed…
Anomaly detection in multivariate time series data is of paramount importance for ensuring the efficient operation of large-scale systems across diverse domains. However, accurately detecting anomalies in such data poses significant…
In recent years, the segmentation of short molecular trajectories with varying diffusive properties has drawn particular attention of researchers, since it allows studying the dynamics of a particle. In the past decade, machine learning…
The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Some asymptotic properties of a Brownian motion in multifractal time, also called multifractal random walk, are established. We show the almost sure and $L^1$ convergence of its structure function. This is an issue directly connected to the…
We use Molecular Dynamics combined with Dissipative Particle Dynamics to construct a model of a binary mixture where the two species differ only in their dynamic properties (friction coefficients). For an asymmetric mixture of slow and fast…
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.…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…
In this work we propose a one-class self-supervised method for anomaly segmentation in images that benefits both from a modern machine learning approach and a more classic statistical detection theory. The method consists of four phases.…
Diffusion models (DMs) have emerged as a powerful class of generative AI models, showing remarkable potential in anomaly detection (AD) tasks across various domains, such as cybersecurity, fraud detection, healthcare, and manufacturing. The…
Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates…