A circular word, or a necklace, is an equivalence class under conjugation of a word. A fundamental question concerning regularities in standard words is bounding the number of distinct squares in a word of length n. The famous conjecture attributed to Fraenkel and Simpson is that there are at most n such distinct squares, yet the best known upper bound is 1.84n by Deza et al. [Discr. Appl. Math...

Z 2 in the limit L→∞, and study the time it takes two lineages tracing backward in time to coalesce. Our work fills a gap between the finite range migration case of [Ann. Appl. Probab. 15 (2005) 671–699] and the long range case of [Genetics 172 (2006) 701–708], where the migration range is a positive fraction of L. We obtain limit theorems for the intermediate case, and verify a conjecture in [...

Writing academic texts by novice researchers requires a framework and support by learning how to cite the works of others. However, compared to the studies on other academic writings, studying citations by considering certainty markers has received little attention. The main purpose of this study was to investigate the shifts of certainty markers (hedges and boosters) in pre- and post-citation ...

Writing academic texts by novice researchers requires a framework and support by learning how to cite the works of others. However, compared to the studies on other academic writings, studying citations by considering certainty markers has received little attention. The main purpose of this study was to investigate the shifts of certainty markers (hedges and boosters) in pre- and post-citation ...