Related papers: A Mathematical Analysis of Mathematical Faculty
It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making…
Statistics experiences a storm around the perceived misuse and possible abuse of its methods in the context of the so-called reproducibility crisis. The methods and styles of quantification practiced in mathematical modelling rarely make it…
NLP models have progressed drastically in recent years, according to numerous datasets proposed to evaluate performance. Questions remain, however, about how particular dataset design choices may impact the conclusions we draw about model…
It is widely recognized that collaboration between the public and private research sectors should be stimulated and supported, as a means of favoring innovation and regional development. This work takes a bibliometric approach, based on…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…
This paper provides a detailed description of the data collection and machine learning model used in our recent PNAS paper "Flat Teams Drive Scientific Innovation" Xu et al. [2022a]. Here, we discuss how the features of scientific…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
Mathematical reasoning is a fundamental capability for large language models (LLMs), yet achieving high performance in this domain remains a significant challenge. The auto-regressive generation process often makes LLMs susceptible to…
This scoping review examines the use of student explanation strategies in postsecondary mathematics and statistics education. We analyzed 46 peer-reviewed articles published between 2014 and 2024, categorizing student explanations into…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
In this paper we initiate some investigations on MathSciNet database. For many mathematicians this website is used on a regular basis, but surprisingly except for the information provided by MathSciNet itself, there exist almost no…
We present the design and methodology for the large scale hybrid paper recommender system used by Microsoft Academic. The system provides recommendations for approximately 160 million English research papers and patents. Our approach…
Automatic evaluation metrics capable of replacing human judgments are critical to allowing fast development of new methods. Thus, numerous research efforts have focused on crafting such metrics. In this work, we take a step back and analyze…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
This paper proposes a theoretical framework which models the information provided by retrieval systems in terms of Information Theory. The proposed framework allows to formalize: (i) system effectiveness as an information theoretic…
While the ``hierarchy of science'' has been widely analysed, there is no corresponding study of the status of subfields within a given scientific field. We use bibliometric data to show that subfields of mathematics have a different…
Academic performance depends on a multivariable nexus of socio-academic and financial factors. This study investigates these influences to develop effective strategies for optimizing students' CGPA. To achieve this, we reviewed various…
Large-enrollment university courses face persistent challenges in providing timely and scalable instructional support. While generative AI holds promise, its effective use depends on reliability and pedagogical alignment. We present a…