Related papers: f4ncgb: High Performance Gr\"obner Basis Computati…
As a class of emerging post-CMOS technologies, Field-coupled Nanocomputing (FCN) devices promise computation with tremendously low energy dissipation. Even though ground breaking advances in several physical implementations like Quantum-dot…
As computational challenges in optimization and statistical inference grow ever harder, algorithms that utilize derivatives are becoming increasingly more important. The implementation of the derivatives that make these algorithms so…
Sparse linear algebra is a cornerstone of many scientific computing and machine learning applications. Python has become a popular choice for these applications due to its simplicity and ease of use. Yet high performance sparse kernels in…
Graph algorithms play an important role in many computer science areas. In order to solve problems that can be modeled using graphs, it is necessary to use a data structure that can represent those graphs in an efficient manner. On top of…
This text consists of five relatively systematic notes on Gr\"obner bases and free resolutions of modules over solvable polynomial algebras.
We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is…
Binary convolutional neural networks (BCNNs) provide a potential solution to reduce the memory requirements and computational costs associated with deep neural networks (DNNs). However, achieving a trade-off between performance and…
The Pierre Auger Observatory is designed to unveil the nature and the origins of the highest energy cosmic rays. The large and geographically dispersed collaboration of physicists and the wide-ranging collection of simulation and…
The Pierre Auger Observatory is designed to unveil the nature and the origins of the highest energy cosmic rays. The large and geographically dispersed collaboration of physicists and the wide-ranging collection of simulation and…
A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…
In this paper, we obtain respectively some new linear bases of free unitary (modified) weighted differential algebras and free nonunitary (modified) Rota-Baxter algebras, in terms of the method of Gr\"{o}bner-Shirshov bases.
This article introduces 'cpp11armadillo', a new R package that integrates the powerful Armadillo C++ library for linear algebra into the R programming environment. Targeted primarily at social scientists and other non-programmers, this…
We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for…
Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…
fwdpp is a C++ library of routines intended to facilitate the development of forward-time simulations under arbitrary mutation and fitness models. The library design provides a combination of speed, low memory overhead, and modeling…
This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young…
This paper presents a novel framework for graded neural networks (GNNs) built over graded vector spaces $\V_\w^n$, extending classical neural architectures by incorporating algebraic grading. Leveraging a coordinate-wise grading structure…
OpenLB is an object-oriented implementation of LBM. It is the first implementation of a generic platform for LBM programming, which is shared with the open source community (GPLv2). Since the first release in 2007, the code has been…
An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library can handle arbitrary integral expressions on top of $\mathbf{p}$, $\mathbf{r}$…
DiffSharp is an algorithmic differentiation or automatic differentiation (AD) library for the .NET ecosystem, which is targeted by the C# and F# languages, among others. The library has been designed with machine learning applications in…