Related papers: The MathScheme Library: Some Preliminary Experimen…
The Graph Brain Project is an experiment in how the use of automated mathematical discovery software, databases, large collaboration, and systematic investigation provide a model for how mathematical research might proceed in the future.…
Sketching is an important means of communication in software engineering practice. Yet, there is little research investigating the use of sketches. We want to contribute a better understanding of sketching, in particular its use during…
Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
This paper provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element…
First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may…
There is given the program realization system "lexicon" by the using lexicographical procedure.
Large Language Models (LLMs) often struggle with code generation tasks involving niche software libraries. Existing code generation techniques with only human-oriented documentation can fail -- even when the LLM has access to web search and…
The mathematical universe discussed here gives models of possible structures our physical universe can have.
Living labs have been established across different countries to evaluate how the interaction between humans and buildings can be optimized to improve comfort, health, and energy savings. However, existing living labs can be too…
In this paper we suggest how the mathematical concept of hyperstructures may be a useful tool in the study of the higher, hierachical structure of languages.
We introduce \textsc{qcmath}, a user-friendly quantum chemistry software tailored for electronic structure calculations, implemented using the Wolfram Mathematica language and available at \url{https://github.com/LCPQ/qcmath}. This…
Laminate mechanisms are a reliable concept in producing lowcost robots for educational and commercial purposes. These mechanisms are produced using low-cost manufacturing techniques which have improved significantly during recent years and…
We are convinced of the usefulness of sketches and diagrams during mathematical work but the observation is made in our practices that they are not spontaneously used by students. In order to study the understanding and use of sketches by…
Designing algorithms with provable guarantees that also work well in practice remains difficult, requiring both mathematical reasoning and careful implementation. Existing approaches that bridge worst-case theory and empirical performance,…
To build a large library of mathematics, it seems more efficient to take advantage of the inherent structure of mathematical theories. Various theory presentation combinators have been proposed, and some have been implemented, in both…
While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits…
To evaluate software maintenance techniques and tools in controlled experiments with human participants, researchers currently use projects and tasks selected on an ad-hoc basis. This can unrealistically favor their tool, and it makes the…
In our days, the necessity of laboratory apparatus accustoming by building up specific software objects for studying the virtual evolution of physical phenomena is a major request. In this respect, the aim of the present paper is to present…
Computational meshes, as a way to partition space, form the basis of much of PDE simulation technology, for instance for the finite element and finite volume discretization methods. In complex simulations, we are often driven to modify an…