16 papers · ranked by Valyu relevance
Oluwateniayo O. Ogunsan, Daniel Lobo
Mathematical models formally and precisely represent biological mechanisms with complex dynamics. To understand the possible behaviors of such systems, phase portrait diagrams can be used to visualize their overall global dynamics across a domain. However, producing these phase portrait diagrams is a laborious process…
Francesca Bertacchini, Carmelo Scuro, Pietro Pantano, Eleonora Bilotta
'Eleonora Bilotta'] An educational robotics lab has been planned for undergraduate students in an Electronic Engineering degree, using the Project Based Learning (PBL) approach and the NAO robot. Students worked in a research context, with the aim of making the functions of the NAO robot as social and autonomous as…
L. Fekésházy, Bakar Chargeishvili, G. Somogyi, S. Van Thurenhout
We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for the decomposition of rational functions with fully factorized denominators. We provide implementations in both the Wolfram…
Jack Heimrath
The area method is a decision procedure for geometry developed by Chou et al. in the 1990's. The method aims to reduce the specified hypothesis to an algebraically verifiable form by applying elimination lemmas. The order in which the lemmas are applied is determined by the stated conjecture and the underlying…
M. M. Hammad, M. M. Yahia
Optimization, linear algebra, probability, and statistics are cornerstones of machine learning. The majority of current machine learning textbooks concentrate on machine learning techniques and algorithms and presuppose that readers are proficient in mathematics and statistics. The gap between high school mathematics…
Éléa Thibault Greugny, Nicolas Ratto, Loïc Etheve, Jean-Baptise Gourlet + 2 more
Mathematical modeling of disease and drug action is becoming an indispensable component of drug development, underscored by recent examples of models predicting trial results. To be able to rely on such approaches, decision-makers need to be able to verify those results independently with in silico confirmatory…
Ian Briggs, Yash Lad, Pavel Panchekha
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately…
Gideon Baur, Claude Duhr
We introduce IterInt, a novel package implemented in both Mathematica and C++ for the numerical evaluation of iterated integrals involving arbitrary integration kernels. After the user has defined the integration kernels, IterInt transforms the iterated integrals into a system of first-order linear differential…
Amir Hossein Salehi Shayegan
In this work, we present a solution to the critical limitation of qubit capacity in near-term quantum hardware by giving a hybrid framework that integrates the spectral element method (SEM) with distributed quantum computing. Using domain decomposition techniques, the additive and multiplicative Schwarz methods, the…
Cyril Cayron
A new algorithm for lattice reduction based on a series of directional and hyperplanar shears and driven by the decrease of the basis rhombicity is proposed. It can be used to reduce unit cells in dimension 3 and higher.
Daniel McKinley
Elementary cellular automata (ECA) are a set of simple binary programs in the form of truth tables called Wolfram codes that produce complex output when done repeatedly in parallel, and quaternions are an extension of complex numbers frequently used to represent 3D space and its rotations in computer graphics due to…
V. L. Kalmykov, L. V. Kalmykov
Mathematical black box models, which hide the structure and behavior of the subsystems, currently dominate science. Errors and paradoxes, such as the biodiversity paradox and the limiting similarity hypothesis, often arise from subjective interpretations of these hidden mechanisms. To address these problems, we have…
Arieh Iserles, Georg Maierhofer
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to approximate these integrals in many settings at uniform cost. In this work, we…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Authors not listed
An automatic code generated C++/HIP/CUDA implementation of the (auxiliary) Fock, or Kohn–Sham, matrix construction for execution in GPU-accelerated hardware environments is presented. The module is developed as part the quantum chemistry software package VeloxChem, employing localized Gaussian atomic orbitals. The per-…
Aleksandra Djordjevic, Junhua Li, Shuangsang Fang, Lei Cao + 1 more
This paper introduces a new approach to cell clustering using the Variable Neighborhood Search (VNS) metaheuristic. The purpose of this method is to cluster cells based on both gene expression and spatial coordinates. Initially, we confronted this clustering challenge as an Integer Linear Programming minimization…