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This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the $d$-dimensional Euclidean space. Both the…
In this paper we establish the local and global well-posedness of weak and strong solutions to second order fractional mean-field SDEs with singular/distribution interaction kernels and measure initial value, where the kernel can be Newton…
This study investigates the application of an artificial neural network to predict the complex dielectric properties of granular catalysts commonly used in microwave reaction chemistry. The study utilizes finite element electromagnetic…
Scatter processes of photons lead to blurring of images produced by CT (computed tomography) or CBCT (cone beam computed tomography) in the KV domain or portal imaging in the MV domain (KV: kilovolt age, MV: megavoltage). Multiple scatter…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…
We develop a unified framework for nonparametric functional estimation based on kernel transport along orbits of discrete group actions, which we term \emph{Twin Spaces}. Given a base kernel $K$ and a group $G = \langle\varphi\rangle$…
The morphology of nanostructured materials exhibiting a polydisperse porous space, such as aerogels, is very open porous and fine grained. Therefore, a simulation of the deformation of a large aerogel structure resolving the nanostructure…
Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a…
Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the…
In this work, we investigate the use of deep neural networks (DNNs) as surrogates for solving the inverse acoustic scattering problem of recovering a sound-soft obstacle from phaseless far-field measurements. We approximate the forward maps…
Modeling the propagation of light through disordered media is central to understanding and controlling wave transport in diverse optical and mesoscopic applications. Here, we present a random matrix simulation framework for modeling the…
Existing measures and representations for trajectories have two longstanding fundamental shortcomings, i.e., they are computationally expensive and they can not guarantee the `uniqueness' property of a distance function: dist(X,Y) = 0 if…
We show that it is possible to reconcile NMR and neutron scattering experiments on both LSCO and YBCO, by making use of the Millis-Monien-Pines mean field phenomenological expression for the dynamic spin-spin response function, and…
We discuss the radiative corrections to charged and neutral current deep-inelastic neutrino--nucleon scattering in the minimal supersymmetric standard model (MSSM). In particular, deviations from the Standard Model prediction for the ratios…
Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant…
A new algorithm to perform coherent mode decomposition of the undulator radiation is proposed. It is based in separating the horizontal and vertical directions, reducing the problem by working with one-dimension wavefronts. The validity…
Motion artifacts present a significant challenge in structural MRI (sMRI), often compromising clinical diagnostics and large-scale automated analysis. While manual quality control (QC) remains the gold standard, it is increasingly…
Data-driven neural networks are increasingly used as surrogate forward models in geophysics, but it remains unclear whether they recover only the data mapping or also the underlying physical sensitivity structure. Here we test this question…
This paper introduces significant advancements in fractional neural operators (FNOs) through the integration of adaptive hybrid kernels and stochastic multiscale analysis. We address several open problems in the existing literature by…