Related papers: Some instructive mathematical errors
Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…
Despite the importance of having a measure of confidence in recommendation results, it has been surprisingly overlooked in the literature compared to the accuracy of the recommendation. In this dissertation, I propose a model calibration…
Grammatical error correction tools are effective at correcting grammatical errors in users' input sentences but do not provide users with \textit{natural language} explanations about their errors. Such explanations are essential for helping…
The increasing reliance on Large Language Models (LLMs) across various domains extends to education, where students progressively use generative AI as a tool for learning. While prior work has examined LLMs' mathematical ability, their…
Across multiple language pairings (English $\to$ \{Spanish, French, German, Mandarin, Japanese, Urdu, Cantonese\}), we find reasoning errors in translation. To quantify how often these reasoning errors occur, we leverage an automated…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
This project investigated new approaches and technologies to enhance the accessibility of mathematical content and its semantic information for a broad range of information retrieval applications. To achieve this goal, the project addressed…
Due to the implement of guardrails by developers, Large language models (LLMs) have demonstrated exceptional performance in explicit bias tests. However, bias in LLMs may occur not only explicitly, but also implicitly, much like humans who…
References, the mechanism scientists rely on to signal previous knowledge, lately have turned into widely used and misused measures of scientific impact. Yet, when a discovery becomes common knowledge, citations suffer from obliteration by…
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…
Machine learning (ML) models that achieve high average accuracy can still underperform on semantically coherent subsets ("slices") of data. This behavior can have significant societal consequences for the safety or bias of the model in…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
This study introduces an approach to estimate the uncertainty in bibliometric indicator values that is caused by data errors. This approach utilizes Bayesian regression models, estimated from empirical data samples, which are used to…
A great many tools have been developed for supervised classification, ranging from early methods such as linear discriminant analysis through to modern developments such as neural networks and support vector machines. A large number of…
There are various mathematical models proposed in the recent literature for estimating the h-index through bibliometric measures, such as number of articles (P) and citations received (C). These models have been previously empirically…
As large language models take on growing roles as automated evaluators in practical settings, a critical question arises: Can individuals persuade an LLM judge to assign unfairly high scores? This study is the first to reveal that…
Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
Fifteen years of research studies have concluded unanimously that spreadsheet errors are both common and non-trivial. Now we must seek ways to reduce spreadsheet errors. Several approaches have been suggested, some of which are promising…
The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its…