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The basis of the discrete element method is to model masses interacting with each other through different forces and constraints. On each mass, the second law of Newton is applied to obtain a differential equation. From this equation and boundary condition ...
The Pictorial Usability Inventory (PUI) is an image-based instrument that was designed for the assessment of perceived usability of smartphone apps. The aim was to provide users with an easy and intuitive access to the evaluation of perceived usability. PU ...
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike ...
Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, the ...
We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides a prototype of ...
We study continuous-domain linear inverse problems with generalized total-variation (gTV) regularization, expressed in terms of a regularization operator L. It has recently been proved that such inverse problems have sparse spline solutions, with fewer jum ...
Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff-Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refin ...
We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spa ...
We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks (ANNs), applicable to dynamical systems arising from Ordinary Differential Equations (ODEs) or time-dependent Partial Differential Equations (PDEs). Unlike ...