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Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components,…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
Computing students increasingly rely on generative AI tools for programming assistance, often without formal instruction or guidance. This highlights a need to teach students how to effectively interact with AI models, particularly through…
Developing software to effectively take advantage of growth in parallel and distributed processing capacity poses significant challenges. Traditional programming techniques allow a user to assume that execution, message passing, and memory…
The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…
In this work we propose a new type of shift spaces, called blur shift spaces, where one can represent with a single symbol an entire set of infinite symbols. Such shift spaces are constructed from classical shift spaces, by choosing some…
We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by iteration of a 2-dimensional topological substitution. We prove…
This paper presents Tree Notation, a new simple, universal syntax. Language designers can invent new programming languages, called Tree Languages, on top of Tree Notation. Tree Languages have a number of advantages over traditional…
High Performance Computing is notorious for its long and expensive software development cycle. To address this challenge, we present Bind: a "partitioned global workflow" parallel programming model for C++ applications that enables quick…
ColorFull, a C++ package for treating QCD color structure, is presented. ColorFull, which utilizes the trace basis approach, is intended for interfacing with event generators, but can also be used as a stand-alone package for squaring QCD…
We initiate the study of enumerating linear subspaces of alternating matrices over finite fields with explicit coordinates. We postulate that this study can be viewed as a linear algebraic analogue of the classical topic of enumerating…
We present an overview of the implementation of symmetric functions in MuPAD-Combinat. We also explain how to interface C++ programs with MuPAD in order to make efficient research during concrete work sessions.
Template metaprogramming is a popular technique for implementing compile time mechanisms for numerical computing. We demonstrate how expression templates can be used for compile time symbolic differentiation of algebraic expressions in C++…
Tilings and tiling systems are an abstract concept that arise both as a computational model and as a dynamical system. In this paper, we characterize the sets of periods that a tiling system can produce. We prove that up to a slight…
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are a useful tool for designing meaningful data-reduction…
Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…
This article introduces Newton, a specification language for notating the analytic form, units of measure, and sensor signal properties for physical-object-specific invariants and general physical laws. We designed Newton to provide a means…
latfield2 is a C++ library designed to simplify writing parallel codes for solving partial differen- tial equations, developed for application to classical field theories in particle physics and cosmology. It is a significant rewrite of the…