QuestionBank: creating a corpus of parse-annotated questions

This paper describes the development of QuestionBank, a corpus of 4000 parse-annotated questions for (i) use in training parsers employed in QA, and (ii) evaluation of question parsing. We present a series of experiments to investigate the effectiveness of QuestionBank as both an exclusive and supplementary training resource for a state-of-the-art parser in parsing both question and non-question test sets. We introduce a new method for recovering empty nodes and their antecedents (capturing long distance dependencies) from parser output in CFG trees using LFG f-structure reentrancies. Our main findings are (i) using QuestionBank training data improves parser performance to 89.75% labelled bracketing f-score, an increase of almost 11% over the baseline; (ii) back-testing experiments on non-question data (Penn-II WSJ Section 23) shows that the retrained parser does not suffer a performance drop on non-question material; (iii) ablation experiments show that the size of training material provided by QuestionBank is sufficient to achieve optimal results; (iv) our method for recovering empty nodes captures long distance dependencies in questions from the ATIS corpus with high precision (96.82%) and low recall (39.38%). In summary, QuestionBank provides a useful new resource in parser-based QA research

Constructions of biangular tight frames and their relationships with equiangular tight frames

We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular Tight Frames (ETFs) - basis-like systems which admit exactly one frame angle. We demonstrate a smooth parametrization BTFs, where the corresponding frame angles transform smoothly with the parameter, which "passes through" an ETF answers two questions regarding the rigidity of BTFs. We also develop a general framework of so-called harmonic BTFs and Steiner BTFs - which includes the equiangular cases, surprisingly, the development of this framework leads to a connection with the famous open problem(s) regarding the existence of Mersenne and Fermat primes. Finally, we construct a (chordally) biangular tight set of subspaces (ie, a tight fusion frame) which "Pl\"ucker embeds" into an ETF.Comment: 19 page

Strong domain variation and treebank-induced LFG resources

In this paper we present a number of experiments to test the portability of existing treebank induced LFG resources. We test the LFG parsing resources of Cahill et al. (2004) on the ATIS corpus which represents a considerably different domain to the Penn-II Treebank Wall Street Journal sections, from which the resources were induced. This testing shows an under-performance at both c- and f-structure level as a result of the domain variation. We show that in order to adapt the LFG resources of Cahill et al. (2004) to this new domain, all that is necessary is to retrain the c-structure parser on data from the new domain

Fibonacci determinants

Fibonacci numbers don\u27t occur everywhere but they can arise in unexpected places, such as Hessenberg matrices. (You don\u27t know what a Hessenberg matrix is? Better find out!