Paul Barry

Radica Bojičić, Marko D. Petković, Paul Barry

This paper provides the connection between the Hankel transform and aerating transforms of a given integer sequence. Results obtained are used to establish a completely different Hankel transform evaluation of the series reversion of a certain rational function $Q(x)$ and shifted sequences, recently published in our paper \cite{part1}. For that purpose, we needed to evaluate the Hankel transforms of the sequences $\seqn{α^2 C_n-βC_{n+1}}$ and $\seqn{α^2 C_{n+1}-βC_{n+2}}$, where $C=\seqn{C_n}$ is the well-known sequence of Catalan numbers. This generalizes the results of Cvetkovi\' c, Rajković and Ivković \cite{CRI}. Also, we need the evaluation of Hankel-like determinants whose entries are Catalan numbers $C_n$ and which is based on the recent results of Krattenthaler \cite{krattCat}. The results obtained are general and can be applied to many other Hankel transform evaluations.

Paul Barry, Sam Henry, Meliha Yetisgen et al.

We hypothesize that explicit integration of contextual information into an Multi-task Learning framework would emphasize the significance of context for boosting performance in jointly learning Named Entity Recognition (NER) and Relation Extraction (RE). Our work proves this hypothesis by segmenting entities from their surrounding context and by building contextual representations using each independent segment. This relation representation allows for a joint NER/RE system that achieves near state-of-the-art (SOTA) performance on both NER and RE tasks while beating the SOTA RE system at end-to-end NER & RE with a 49.07 F1.