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In recent years, stochastic parametrizations have been ubiquitous in modelling uncertainty in fluid dynamics models. One source of model uncertainty comes from the coarse graining of the fine-scale data and is in common usage in…
The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time…
Probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account.…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
We study the surface growth generated by the random deposition of particles of different sizes. A model is proposed where the particles are aggregated on an initially flat surface, giving rise to a rough interface and a porous bulk. By…
There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…
Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…
Occupied truck parking lots regularly cause hazardous situations. Estimation of current parking lot state could be utilized to provide drivers parking recommendations. In this work, we highlight based on a simulation scenario, how sparse…
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation…
Vehicle-sharing systems are becoming important for urban transportation. In these systems, users arrive at a station, pick up a vehicle, use it for a while and then return it to another station of their choice. Depending on the type of…
The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a…
We propose a mathematical methodology to derive a stochastic parameterization of bulk warm cloud micro-physics properties. Unlike previous bulk parameterizations, the stochastic parameterization does not assume any particular droplet size…
A predecessor pilot (Cacioli, 2026) found that Llama-3-8B implements prompted sandbagging as positional collapse rather than answer avoidance. However, fixed option ordering in MMLU-Pro left open whether this reflected a model-level…
We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common…
Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using…