Search results for "WORDS"
showing 10 items of 562 documents
On the Structure of Bispecial Sturmian Words
2013
A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, that are the digital approximations of Euclidean segments in the plane. In 1997, J. Berstel and A. de Luca proved that \emph{palindromic} bispecial Sturmian words are precisely the maximal internal factors of \emph{primitive} Christoffel words. We extend this result by showing that bispecial Sturmian wo…
On prefix normal words and prefix normal forms
2016
A $1$-prefix normal word is a binary word with the property that no factor has more $1$s than the prefix of the same length; a $0$-prefix normal word is defined analogously. These words arise in the context of indexed binary jumbled pattern matching, where the aim is to decide whether a word has a factor with a given number of $1$s and $0$s (a given Parikh vector). Each binary word has an associated set of Parikh vectors of the factors of the word. Using prefix normal words, we provide a characterization of the equivalence class of binary words having the same set of Parikh vectors of their factors. We prove that the language of prefix normal words is not context-free and is strictly contai…
Mahonian STAT on words
2016
In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…
Open and Closed Prefixes of Sturmian Words
2013
A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We deal with the sequence of open and closed prefixes of Sturmian words and prove that this sequence characterizes every finite or infinite Sturmian word up to isomorphisms of the alphabet. We then characterize the combinatorial structure of the sequence of open and closed prefixes of standard Sturmian words. We prove that every standard Sturmian word, after swapping its first letter, can be written as an infinite product of squares of reversed standard words.
Constructing Antidictionaries in Output-Sensitive Space
2021
A word $x$ that is absent from a word $y$ is called minimal if all its proper factors occur in $y$. Given a collection of $k$ words $y_1,y_2,\ldots,y_k$ over an alphabet $\Sigma$, we are asked to compute the set $\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ of minimal absent words of length at most $\ell$ of word $y=y_1\#y_2\#\ldots\#y_k$, $\#\notin\Sigma$. In data compression, this corresponds to computing the antidictionary of $k$ documents. In bioinformatics, it corresponds to computing words that are absent from a genome of $k$ chromosomes. This computation generally requires $\Omega(n)$ space for $n=|y|$ using any of the plenty available $\mathcal{O}(n)$-time algorithms. This is because a…
Languages with mismatches and an application to approximate indexing
2005
In this paper we describe a factorial language, denoted by L(S, k,r), that contains all words that occur in a string 5 up to k mismatches every r symbols. Then we give some combinatorial properties of a parameter, called repetition index and denoted by R(S,k,r), defined as the smallest integer h ? 1 such that all strings of this length occur at most in a unique position of the text S up to k mismatches every r symbols. We prove that R(S, k, r) is a non-increasing function of r and a non-decreasing function of k and that the equation r = R(S, k, r) admits a unique solution. The repetition index plays an important role in the construction of an indexing data structure based on a trie that rep…
Atypical perceptual narrowing in prematurely born infants is associated with compromised language acquisition at 2 years of age
2010
Abstract Background Early auditory experiences are a prerequisite for speech and language acquisition. In healthy children, phoneme discrimination abilities improve for native and degrade for unfamiliar, socially irrelevant phoneme contrasts between 6 and 12 months of age as the brain tunes itself to, and specializes in the native spoken language. This process is known as perceptual narrowing, and has been found to predict normal native language acquisition. Prematurely born infants are known to be at an elevated risk for later language problems, but it remains unclear whether these problems relate to early perceptual narrowing. To address this question, we investigated early neurophysiolog…
Zirconia in fixed prosthesis. A literature review
2014
Statement of problem: Evidence is limited on the efficacy of zirconia-based fixed dental prostheses. Objective: To carry out a literature review of the behavior of zirconium oxide dental restorations. Material and Methods: This literature review searched the Pubmed, Scopus, Medline and Cochrane Library databases using key search words “zirconium oxide,” “zirconia,” “non-metal restorations,” “ceramic oxides,” “veneering ceramic,” “zirconia-based fixed dental prostheses”. Both in vivo and in vitro studies into zirconia-based prosthodontic restoration behavior were included. Results: Clinical studies have revealed a high rate of fracture for porcelain-veneered zirconia-based restorations that …
La sufixació apreciativa del català: creacions lèxiques i implicacions morfològiques
2015
Resum: La situació de la derivació apreciativa dins la morfologia és excepcional, perquè la informació limitada que contenen, en general, les gramàtiques i els diccionaris sobre els apreciatius així com l’ús habitual d’aquestes formes en contextos familiars i informals fan que la creativitat dels parlants no es vegi limitada per normatives i que, per tant, aflorin solucions imaginatives, que, tot i la variació existent, segueixen uns condicionaments gramaticals clars. L’objectiu d’aquest treball és aportar noves dades en aquest camp a partir de formes recollides en corpus tradicionals i per internet, amb una doble finalitat: d’una banda, aprofundir en les particularitats morfològiques de la…
Evaluation of a short food frequency questionnaire used among Norwegian children.
2012
Objective: The aim of this study was to evaluate a short food frequency questionnaire (FFQ) against a four-day precoded food diary (PFD) with regard to frequency of food intake among Norwegian 9- and 13-year-olds. Subjects and design: A total of 733 9-year-olds and 904 13-year-olds completed first a short FFQ and one to two weeks later a four-day PFD. The short FFQ included questions about 23 food items, including different drinks, fruits, vegetables, bread, fish, pizza, sweets, chocolate and savoury snacks. The PFD covered the whole diet. Results: When comparing mean intake from the PFD with comparable food items in the FFQ, all food items showed that increasing intake measured with the PF…