Related papers: Boosting Vector Calculus with the Graphical Notati…
A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
This paper introduces a new approach to extract and analyze vector data from technical drawings in PDF format. Our method involves converting PDF files into SVG format and creating a feature-rich graph representation, which captures the…
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
In the rapidly evolving interdisciplinary field of quantum information science and technology, a major obstacle is the need to understand advanced mathematics to solve complex problems. Current findings in educational research suggest that…
With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines…
In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between…
Multi-task learning in text classification leverages implicit correlations among related tasks to extract common features and yield performance gains. However, most previous works treat labels of each task as independent and meaningless…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
Computer science's increased recognition as a prominent field of study has attracted students with diverse academic backgrounds. This has significantly increased the already high failure rates in introductory courses. To address this…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
In one of his books [$\textit{The Feynmann Lectures on Physics}$, vol. 2], Feynman presents a didactic approach to introduce basic ideas about tensors, using, as a first example, the dependence of the induced polarization of a crystal on…
We present a new approach for recognition of complex graphic symbols in technical documents. Graphic symbol recognition is a well known challenge in the field of document image analysis and is at heart of most graphic recognition systems.…
Although physics has become increasingly computational, with computing even being considered the third pillar of physics, it is still not well integrated into physics education. Research suggests that integrating Computational Thinking (CT)…
Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical…
Technology has helped to innovate in the teaching-learning process. Today's students are more demanding actors when it comes to the environment, they have at their disposal to learn, experiment and develop critical thinking. The area of…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
Vector-space word representations obtained from neural network models have been shown to enable semantic operations based on vector arithmetic. In this paper, we explore the existence of similar information on vector representations of…