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The diffusion model has emerged as a powerful tool for generating atomic structures for materials science. This work calls attention to the deficiency of current particle-based diffusion models, which represent atoms as a point cloud, in…
The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian. However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to…
Machine learning has demonstrated remarkable promise for solving the trajectory generation problem and in paving the way for online use of trajectory optimization for resource-constrained spacecraft. However, a key shortcoming in current…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
Urban forests play a key role in enhancing environmental quality and supporting biodiversity in cities. Mapping and monitoring these green spaces are crucial for urban planning and conservation, yet accurately detecting trees is challenging…
Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the…
Global Navigation Satellite Systems (GNSS) are vital for reliable urban positioning. However, multipath and non-line-of-sight reception often introduce large measurement errors that degrade accuracy. Learning-based methods for predicting…
Diffusion models have achieved outstanding performance in unsupervised industrial anomaly detection (uIAD) by learning a manifold of normal data under the common assumption that off-manifold anomalies are harder to generate, resulting in…
With the growing complexity of cyberattacks targeting critical infrastructures such as water treatment networks, there is a pressing need for robust anomaly detection strategies that account for both system vulnerabilities and evolving…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long…
We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for…
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…
Change point detection has become an important part of the analysis of the single-particle tracking data, as it allows one to identify moments, in which the motion patterns of observed particles undergo significant changes. The segmentation…
Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the…
We theoretically analyze diffusion trajectories of an anisotropic object moving on a two dimensional space in the absence of an external field. In determining diffusion parameters associated with the shape anisotropy, we devise a measure…
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in…
Inferring transient molecular structural dynamics from diffraction data is an ambiguous task that often requires different approximation methods. In this paper we present an attempt to tackle this problem using machine learning. While most…
Diffusion is modeled on the recently proposed Hanoi networks by studying the mean- square displacement of random walks with time, <r^2>~t^{2/d_w}. It is found that diffusion - the quintessential mode of transport throughout Nature -…