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Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…
In this work, algorithms for the parallel computation of three-body interactions in molecular dynamics are developed. While traversals for the computation of pair interactions are readily available in the literature, here, such traversals…
When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance…
The demand for high-performance computing (HPC) is ever-increasing for everyday statistical computing purposes. The downside is that we need to write specialized code for each HPC environment. CPU-level parallelization needs to be…
We present the software design of Gridap, a novel finite element library written exclusively in the Julia programming language, which is being used by several research groups world-wide to simulate complex physical phenomena such as…
As GPU-accelerated mathematical programming techniques mature, there is growing interest in utilizing them to address the computational challenges of power system optimization. This paper introduces ExaModelsPower.jl, an open-source…
We introduce JAX MD, a software package for performing differentiable physics simulations with a focus on molecular dynamics. JAX MD includes a number of physics simulation environments, as well as interaction potentials and neural networks…
A generalization of the filled-in Julia set is presented using the multicomplex numbers and an algorithm is presented to visualize these sets in the tridimensional space. There are many ways to visualize these higher dimensional fractals…
Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis,…
Machine-learned interatomic potentials (MLIPs) are revolutionizing computational materials science and chemistry by offering an efficient alternative to {\em ab initio} molecular dynamics (MD) simulations. However, fitting high-quality…
In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…
The increase in non-renewable energy consumption and CO2 emissions, especially in the manufacturing sector, is moving radical shifts in energy supply policies and production models. Renewable energy integration and regulated pricing…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
Kinetic plasma processes, such as magnetic reconnection, collisionless shocks, and turbulence, are fundamental to the dynamics of astrophysical and laboratory plasmas. Simulating these processes often requires particle-in-cell (PIC)…
Current mathematical frameworks for predicting the flux state and macromolecular composition of the cell do not rely on thermodynamic constraints to determine the spontaneous direction of reactions. These predictions may be biologically…
Jupyter Notebook is an interactive development environment commonly used for rapid experimentation of machine learning (ML) solutions. Describing the ML activities performed along code cells improves the readability and understanding of…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
The integration of converter-interfaced generation (CIG) from renewable energy sources poses challenges to the stability and transient behavior of electric power systems. Understanding the dynamic behavior of low-inertia power systems is…