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Artificial Intelligence (AI) has witnessed rapid growth, especially in the subfields Natural Language Processing (NLP), Machine Learning (ML) and Computer Vision (CV). Keeping pace with this rapid progress poses a considerable challenge for…
We introduce ArGoT, a data set of mathematical terms extracted from the articles hosted on the arXiv website. A term is any mathematical concept defined in an article. Using labels in the article's source code and examples from other…
We discuss the main stages of development of the error calculation since the beginning of XIX-th century by insisting on what prefigures the use of Dirichlet forms and emphasizing the mathematical properties that make the use of Dirichlet…
Large Language Models (LLMs) excel at general tasks but underperform in specialized domains like economics and psychology, which require deep, principled understanding. To address this, we introduce ACER (Automated Curriculum-Enhanced…
Sequence transformations are valuable numerical tools that have been used with considerable success for the acceleration of convergence and the summation of diverging series. However, our understanding of their theoretical properties is far…
The exponential growth of scientific production makes secondary literature abridgements increasingly demanding. We introduce a new open-source framework for systematic reviews that significantly reduces time and workload for collecting and…
The number of scientific papers grows exponentially in many disciplines. The share of online available papers grows as well. At the same time, the period of time for a paper to loose at chance to be cited anymore shortens. The decay of the…
Background: Machine learning algorithms are widely used to predict defect prone software components. In this literature, computational experiments are the main means of evaluation, and the credibility of results depends on experimental…
It may seem surprising that, out of all areas of science, computer scientists have been slow to post electronic versions of papers on sites like arXiv.org. Instead, computer scientists have tended to place papers on our individual home…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…
We show that for any fixed integer $k \geq 0$, there exists an algorithm that computes the diameter and the eccentricies of all vertices of an input unweighted, undirected $n$-vertex graph of Euler genus at most $k$ in time \[…
Let $V$ be a closed subscheme of a projective space $\mathbb{P}^n$. We give an algorithm to compute the Chern-Schwartz-MacPherson class, Euler characteristic and Segre class of $ V$. The algorithm can be implemented using either symbolic or…
In this article, we study Euler characteristic techniques in topological data analysis. Pointwise computing the Euler characteristic of a family of simplicial complexes built from data gives rise to the so-called Euler characteristic…
In this paper we present a new mathematical conception based on a new method for ordering the integers. The method relies on the assumption that negative numbers are beyond infinity, which goes back to Wallis and Euler. We also present a…
The identification and localization of errors is a core task in peer review, yet the exponential growth of scientific output has made it increasingly difficult for human reviewers to reliably detect errors given the limited pool of experts.…
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give…
This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction…
Without accurate transcription of numerical data in scientific documents, a scientist cannot draw accurate conclusions. Unfortunately, the process of copying numerical data from one paper to another is prone to human error. In this paper,…
This paper summarizes the work on implementing few solutions for the Steiner Tree problem which we undertook in the PAAL project. The main focus of the project is the development of generic implementations of approximation algorithms…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…