Related papers: From Euler to Today: Universal Mathematical Fallib…
We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…
Large language models can generate scientific simulation code, but the generated code silently fails on most non-textbook problems. We show that classical mathematical validation -- well-posedness, convergence, and error certification --…
We extract mathematical concepts from mathematical text using generative large language models (LLMs) like ChatGPT, contributing to the field of automatic term extraction (ATE) and mathematical text processing, and also to the study of LLMs…
Researchers working in lattice field theory constitute an established community since the early 1990s, and around the same time the online open-access e-print repository arXiv was created. The fact that this field has a specific arXiv…
In recent years, funding agencies and journals increasingly advocate for open science practices (e.g. data and method sharing) to improve the transparency, access, and reproducibility of science. However, quantifying these practices at…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…
We report on a novel algorithm for controlling global error in a step-by-step (stepwise) sense, in the numerical solution of a scalar, autonomous, nonstiff or weakly stiff problem. The algorithm exploits the remainder term of a Taylor…
As more and more academic papers are being submitted to conferences and journals, evaluating all these papers by professionals is time-consuming and can cause inequality due to the personal factors of the reviewers. In this paper, in order…
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…
Peer reviewing is a central component in the scientific publishing process. We present the first public dataset of scientific peer reviews available for research purposes (PeerRead v1) providing an opportunity to study this important…
This work proposes a novel approach to text categorization -- for unknown categories -- in the context of scientific literature, using Natural Language Processing techniques. The study leverages the power of pre-trained language models,…
Extracting information from big data sets, both real and simulated, is a modern hallmark of the physical sciences. In practice, students face barriers to learning ``Big Data'' methods in undergraduate physics and astronomy curricula. As an…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument (Y less than 0.1).…
The LLM Wiki pattern, to compile and provide domain knowledge into a persistent artifact and serve it to LLMs via KV cache inference, promises context access at sub-second latency with zero retrieval failure. Realizing this requires solving…
AI generated content (AIGC) presents considerable challenge to educators around the world. Instructors need to be able to detect such text generated by large language models, either with the naked eye or with the help of some tools. There…
Context: The constant growth of primary evidence and Systematic Literature Reviews (SLRs) publications in the Software Engineering (SE) field leads to the need for SLR Updates. However, searching and selecting evidence for SLR updates…
In this note we derive large-scale regularity properties of solutions to second-order linear elliptic equations with random coefficients on the half- space with homogeneous Neumann boundary data; it is a companion to arXiv:1604.02717 in…
Translation from the Latin original, "Inventio summae cuiusque seriei ex dato termino generali" (1735). E47 in the Enestrom index. In this paper Euler derives the Euler-Maclaurin summation formula, by expressing y(x-1) with the Taylor…
We provide a writeup of a resolution of Erd\H{o}s Problem #728; this is the first Erd\H{o}s problem (a problem proposed by Paul Erd\H{o}s which has been collected in the Erd\H{o}s Problems website) regarded as fully resolved autonomously by…