Recurrent Partial Words

Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite partial word w, the number of distinct full words over the alphabet that are compatible with factors of w of length n, called subwords of w, refers to a measure of complexity of infinite partial words so-called subword complexity. This measure is of particular interest because we can construct partial words with subword complexities not achievable by full words. In this paper, we consider the notion of recurrence over infinite partial words, that is, we study whether all of the finite subwords of a given infinite partial word appear infinitely often, and we establish connections between subword complexity and recurrence in this more general framework

Recurrent Partial Words

Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite partial word w, the number of distinct full words over the alphabet that are compatible with factors of w of length n, called subwords of w, refers to a measure of complexity of infinite partial words so-called subword complexity. This measure is of particular interest because we can construct partial words with subword complexities not achievable by full words. In this paper, we consider the notion of recurrence over infinite partial words, that is, we study whether all of the finite subwords of a given infinite partial word appear infinitely often, and we establish connections between subword complexity and recurrence in this more general framework.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Inflammatory myofibroblastic tumor of the bladder: dramatic presentation of an unusual tumor

We report a case of an inflammatory myofibroblastic tumor of the bladder (IMT) in an adult male who presented with recurrent hematuria. He required partial cystectomy which revealed perivesical fat infiltration. In spite of this, the tumor was categorized as benign and the patient remained symptom- and tumor-free 18 months post-operatively.Key Words: Myofibroblastic tumor, bladder, IM

Abelian-Square-Rich Words

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain at most $\Theta(n^2)$ distinct factors, and there exist words of length $n$ containing $\Theta(n^2)$ distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length $n$ grows quadratically with $n$. More precisely, we say that an infinite word $w$ is {\it abelian-square-rich} if, for every $n$, every factor of $w$ of length $n$ contains, on average, a number of distinct abelian-square factors that is quadratic in $n$; and {\it uniformly abelian-square-rich} if every factor of $w$ contains a number of distinct abelian-square factors that is proportional to the square of its length. Of course, if a word is uniformly abelian-square-rich, then it is abelian-square-rich, but we show that the converse is not true in general. We prove that the Thue-Morse word is uniformly abelian-square-rich and that the function counting the number of distinct abelian-square factors of length $2n$ of the Thue-Morse word is $2$-regular. As for Sturmian words, we prove that a Sturmian word $s_{\alpha}$ of angle $\alpha$ is uniformly abelian-square-rich if and only if the irrational $\alpha$ has bounded partial quotients, that is, if and only if $s_{\alpha}$ has bounded exponent.Comment: To appear in Theoretical Computer Science. Corrected a flaw in the proof of Proposition

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.Comment: To appear in the proceedings of WORDS 201

Learning Multi-Level Information for Dialogue Response Selection by Highway Recurrent Transformer

With the increasing research interest in dialogue response generation, there is an emerging branch formulating this task as selecting next sentences, where given the partial dialogue contexts, the goal is to determine the most probable next sentence. Following the recent success of the Transformer model, this paper proposes (1) a new variant of attention mechanism based on multi-head attention, called highway attention, and (2) a recurrent model based on transformer and the proposed highway attention, so-called Highway Recurrent Transformer. Experiments on the response selection task in the seventh Dialog System Technology Challenge (DSTC7) show the capability of the proposed model of modeling both utterance-level and dialogue-level information; the effectiveness of each module is further analyzed as well