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Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. For example, Aphasia Quotient (AQ) is a critical measure of language impairment and informs…
Ultrafast dynamical processes in photoexcited molecules can be observed with pump-probe measurements, in which information about the dynamics is obtained from the transient signal associated with the excited state. Background signals…
Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterised for the first time in a kinetic collisional framework in the Mach number range $2\le M\le 10$. Our…
This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the \textsc{B}ayesian framework with the \textsc{M}arkov Chain \textsc{M}onte…
Our work is motivated by the analysis of ash plume dynamics, arising in the study of volcanic eruptions. Such phenomena are characterized by large Reynolds number (exceeding $10^7$) and a large number of polydispersed particles~[1]. Thus,…
Stochastic models of varying complexity have been proposed to describe the dispersion of particles in turbulent flows, from simple Brownian motion to complex temporally and spatially correlated models. A method is needed to compare…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
The present study examines the possibility of numerical simulation of a strong shock wave propagating over the surface of a dense layer of particles poured onto an impermeable wall using the Baer-Nunizato two-phase flow model. The setting…
We present a new Eulerian framework for the computation of turbulent compressible multiphase channel flows, specifically to assess turbulence modulation by dispersed particulate matter in dilute concentrations but with significant mass…
In multivariate spline regression, the number and locations of knots influence the performance and interpretability significantly. However, due to non-differentiability and varying dimensions, there is no desirable frequentist method to…
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of…
The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. To describe these phenomena, the two-layer shallow-water equations is commonly employed. When one layer is significantly…
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
We calculate the equation of state of dense deuterium with two ab initio simulations techniques, path integral Monte Carlo and density functional theory molecular dynamics, in the density range of 0.67 < rho < 1.60 g/cc. We derive the…
A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of $\mathbb{R}^n$ or a stationary Poisson…
Shock tube experiments, paired with precision laser diagnostics, are ideal venues to provide kinetics data critically needed for the development, validation and optimization of modern combustion kinetics models. However, to design…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a…
Bayesian estimation with an explicit transitional prior is required for a tracking algorithm to be embedded in most multi-target tracking frameworks. This paper describes a novel approach capable of tracking maneuvering spacecraft with an…