Related papers: f4ncgb: High Performance Gr\"obner Basis Computati…
Using evaluation at appropriately chosen points, we propose a Gr\"obner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the…
This paper shows among other things that over a non-commutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions.
We introduce the Macaulay2 package BooleanGB, which computes a Gr\"obner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…
Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, we apply discretization-invariant neural operators to learn…
We have developed a new tool for numerical work in General Relativity: GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the framework of Differential Geometry to provide a robust and general way of computing on…
Several constructive homological methods based on noncommutative Gr\"obner bases are known to compute free resolutions of associative algebras. In particular, these methods relate the Koszul property for an associative algebra to the…
We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that…
Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the…
We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…
Quantum++ is a modern general-purpose multi-threaded quantum computing library written in C++11 and composed solely of header files. The library is not restricted to qubit systems or specific quantum information processing tasks, being…
The main purpose of this paper is to propose six programs in C++ for matrix computations and solving recurrent equations systems with entries in min plus algebra.
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional…
The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of…
We describe BayesMix, a C++ library for MCMC posterior simulation for general Bayesian mixture models. The goal of BayesMix is to provide a self-contained ecosystem to perform inference for mixture models to computer scientists,…
An explicit C++ library is provided which deals with Zernike Functions over the unit circle as the main subject. The implementation includes basic means to evaluate the functions at points inside the unit circle and to convert the radial…
We present a framework of Training Free Graph Matching (TFGM) to boost the performance of Graph Neural Networks (GNNs) based graph matching, providing a fast promising solution without training (training-free). TFGM provides four widely…
This paper presents alpaqa, an open-source C++ implementation of an augmented Lagrangian method for nonconvex constrained numerical optimization, using the first-order PANOC algorithm as inner solver. The implementation is packaged as an…
Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic…
Operational Neural Networks (ONNs) have recently been proposed as a special class of artificial neural networks for grid structured data. They enable heterogenous non-linear operations to generalize the widely adopted convolution-based…