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GNOLL ("GNOLL's Not *OLL") is a software library for dice notation. Unlike previous papers, GNOLL's dice notation syntax is focused on parsing a language that tabletop role-players and board gamers are already used to for specifying dice…
Traditional attempts for loop closure detection typically use hand-crafted features, relying on geometric and visual information only, whereas more modern approaches tend to use semantic, appearance or geometric features extracted from deep…
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation…
Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…
We propose a new paradigm for modelling and calibrating laser scanners with rotation symmetry, as is the case for Lidars or for galvanometric laser systems with one or two rotating mirrors. Instead of bothering about the intrinsic…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than…
Cross-domain recommendation (CDR) aims to alleviate the data sparsity by transferring knowledge across domains. Disentangled representation learning provides an effective solution to model complex user preferences by separating intra-domain…
We present Scallop, a language which combines the benefits of deep learning and logical reasoning. Scallop enables users to write a wide range of neurosymbolic applications and train them in a data- and compute-efficient manner. It achieves…
Deep Neural Networks (DNNs) are rapidly gaining popularity in a variety of important domains. Formally, DNNs are complicated vector-valued functions which come in a variety of sizes and applications. Unfortunately, modern DNNs have been…
The ability to think abstractly and reason by analogy is a prerequisite to rapidly adapt to new conditions, tackle newly encountered problems by decomposing them, and synthesize knowledge to solve problems comprehensively. We present…
Debugging is a fundamental skill that novice programmers must develop. Numerous tools have been created to assist novice programmers in this process. Recently, large language models (LLMs) have been integrated with automated program repair…
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Algebraic differentiators have attracted much interest in recent years. Their simple implementation as classical finite impulse response digital filters and systematic tuning guidelines may help to solve challenging problems, including, but…
LiDAR-based localization is valuable for applications like mining surveys and underground facility maintenance. However, existing methods can struggle when dealing with uninformative geometric structures in challenging scenarios. This paper…
We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric…