相关论文: A Conversation With Harry Martz

We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the $n$-level correlations of eigenvalues of random unitary matrices as well as a new proof of a formula due to M. Diaconis and P. Shahshahani expressing averages…

As quantum devices scale, quantifying how close an experimental state aligns with a target becomes both vital and challenging. Fidelity is the standard metric, but existing estimators either require full tomography or apply only to…

In an era of radical technology transformations, technology maps play a crucial role in enhancing decision making. These maps heavily rely on automated methods of technology extraction. This paper introduces Retrieval Augmented Technology…

Large language models (LLMs) have shown potential in assisting scientific research, yet their ability to discover high-quality research hypotheses remains unexamined due to the lack of a dedicated benchmark. To address this gap, we…

Mathematicians have traditionally been a select group of academics that produce high-impact ideas allowing substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics…

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and more than 25 books on…

We propose a revisitation of the original experiment performed by H. Hertz in 1888. With a simple setup it is possible to produce electromagnetic waves with a frequency in the range of 3 MHz. By performing Fourier analysis of the signal…

Large Language Models (LLMs) create exciting possibilities for powerful language processing tools to accelerate research in materials science. While LLMs have great potential to accelerate materials understanding and discovery, they…

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods…

The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…

Aerospace manufacturing demands exceptionally high precision in technical parameters. The remarkable performance of Large Language Models (LLMs), such as GPT-4 and QWen, in Natural Language Processing has sparked industry interest in their…

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely…

Code Large Language Models (Code LLMs) have revolutionized software development but raised critical concerns regarding code provenance, copyright protection, and security. Existing code watermarking approaches suffer from two fundamental…

We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…

Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment…

Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number…

TRIZ, the Theory of Inventive Problem Solving, is derived from a comprehensive analysis of patents across various domains, offering a framework and practical tools for problem-solving. Despite its potential to foster innovative solutions,…

The ongoing discussion regarding the utilization of individual research performance for academic hiring, funding allocation, and resource distribution has prompted the need for improved metrics. While traditional measures such as total…

Reproducibility is a cornerstone of scientific research, enabling independent verification and validation of empirical findings. The topic gained prominence in fields such as psychology and medicine, where concerns about non - replicable…

Although Multi-Agent Reinforcement Learning (MARL) is effective for complex multi-robot tasks, it suffers from low sample efficiency and requires iterative manual reward tuning. Large Language Models (LLMs) have shown promise in…