Related papers: FinInG: a package for Finite Incidence Geometry
We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.
Finite-part integration is a recently introduced method of evaluating convergent integrals by means of the finite part of divergent integrals [E.A. Galapon, {\it Proc. R. Soc. A 473, 20160567} (2017)]. Current application of the method…
We introduce FunKit, a Mathematica package for the derivation and tracing of functional equations from arbitrary master equations. FunKit provides an expression vocabulary and a set of rules that allow for derivations in any given field…
simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added,…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
We present FINJ, a high-level fault injection tool for High-Performance Computing (HPC) systems, with a focus on the management of complex experiments. FINJ provides support for custom workloads and allows generation of anomalous conditions…
Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…
The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the…
fgivenx is a Python package for functional posterior plotting, currently used in astronomy, but will be of use to scientists performing any Bayesian analysis which has predictive posteriors that are functions. The source code for fgivenx is…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
We introduce Generalized Integrated Gradients (GIG), a formal extension of the Integrated Gradients (IG) (Sundararajan et al., 2017) method for attributing credit to the input variables of a predictive model. GIG improves IG by explaining a…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
Pyrit is a field simulation software based on the finite element method written in Python to solve coupled systems of partial differential equations. It is designed as a modular software that is easily modifiable and extendable. The…
Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…
During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the…
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 determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
This work presents a novel graph neural network (GNN) architecture, the Feature-specific Interpretable Graph Neural Network (FIGNN), designed to enhance the interpretability of deep learning surrogate models defined on unstructured grids in…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
The Indoor Geometry Generator (IGG) is able to generate automatically simplified indoor geometry and its associated unstructured mesh for Computational Fluid Dynamics (CFD) simulations purposes given very simple user inputs. A large number…