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Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…
Semantic map models visualize systematic relations among semantic functions through graph structures and are widely used in linguistic typology. However, existing construction methods either depend on labor-intensive expert reasoning or on…
This paper investigates how GPT-based tools can assist in building reusable analytical spreadsheet models. After a screening, we evaluate five GPT extensions and select Excel AI by pulsrai.com for detailed testing. Through structured…
Interactive simulation toolkits come in handy when teaching macroeconomic models by facilitating an easy understanding of underlying economic concepts and offering an intuitive approach to the models' comparative statics. Based on the…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
We outline a program in the area of formalization of mathematics to automate theorem proving in algebra and algebraic geometry. We propose a construction of a dictionary between automated theorem provers and (La)TeX exploiting syntactic…
The computer programs most users interact with daily are driven by a graphical user interface (GUI). However, many scientific applications are used with a command line interface (CLI) for the ease of development and increased flexibility…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
These notes give an informal and leisurely introduction to $\mathrm{G}_2$ geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in $7$ dimensions that is the pointwise model for…
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…
We present GenEx, a generative model to explain search results to users beyond just showing matches between query and document words. Adding GenEx explanations to search results greatly impacts user satisfaction and search performance.…
Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.