Duong Tran | Searcharxiv

arXiv2026

Cyclotomic factors of rational necklace functions

Necklace polynomials arise in various fields of mathematics, including combinatorics, Lie theory, and Galois theory over finite fields. Their arithmetic properties have been extensively studied in recent years. In this article, we introduce a new class of rational necklace functions that unifies two well-studied families of polynomials: necklace polynomials and Fekete polynomials. We describe several ways in which cyclotomic polynomials appear as factors of these rational necklace functions. Our results unify and generalize various earlier work on necklace polynomials and on Fekete polynomials. In particular, we describe a surprising phenomenon in which certain Galois groups play a hidden role in the appearance of new cyclotomic factors that are not covered by these previous works.

math.NT↗

arXiv2023

Use GPT-J Prompt Generation with RoBERTa for NER Models on Diagnosis Extraction of Periodontal Diagnosis from Electronic Dental Records

This study explored the usability of prompt generation on named entity recognition (NER) tasks and the performance in different settings of the prompt. The prompt generation by GPT-J models was utilized to directly test the gold standard as well as to generate the seed and further fed to the RoBERTa model with the spaCy package. In the direct test, a lower ratio of negative examples with higher numbers of examples in prompt achieved the best results with a F1 score of 0.72. The performance revealed consistency, 0.92-0.97 in the F1 score, in all settings after training with the RoBERTa model. The study highlighted the importance of seed quality rather than quantity in feeding NER models. This research reports on an efficient and accurate way to mine clinical notes for periodontal diagnoses, allowing researchers to easily and quickly build a NER model with the prompt generation approach.

cs.CL↗