A Multidimensional Critical Factorization Theorem

The Critical Factorization Theorem is one of the principal results in combinatorics on words. It relates local periodicities of a word to its global periodicity. In this paper we give a multidimensional extension of it. More precisely, we give a new proof of the Critical Factorization Theorem, but in a weak form, where the weakness is due to the fact that we loose the tightness of the local repetition order. In exchange, we gain the possibility of extending our proof to the multidimensional case. Indeed, this new proof makes use of the Theorem of Fine and Wilf, that has several classical generalizations to the multidimensional cas

Phenotype and genotype of 87 patients with Mowat-Wilson syndrome and recommendations for care

Mowat-Wilson syndrome (MWS) is a rare intellectual disability/multiple congenital anomalies syndrome caused by heterozygous mutation of the ZEB2 gene. It is generally underestimated because its rarity and phenotypic variability sometimes make it difficult to recognize. Here, we aimed to better delineate the phenotype, natural history, and genotype-phenotype correlations of MWS.MethodsIn a collaborative study, we analyzed clinical data for 87 patients with molecularly confirmed diagnosis. We described the prevalence of all clinical aspects, including attainment of neurodevelopmental milestones, and compared the data with the various types of underlying ZEB2 pathogenic variations.ResultsAll anthropometric, somatic, and behavioral features reported here outline a variable but highly consistent phenotype. By presenting the most comprehensive evaluation of MWS to date, we define its clinical evolution occurring with age and derive suggestions for patient management. Furthermore, we observe that its severity correlates with the kind of ZEB2 variation involved, ranging from ZEB2 locus deletions, associated with severe phenotypes, to rare nonmissense intragenic mutations predicted to preserve some ZEB2 protein functionality, accompanying milder clinical presentations.ConclusionKnowledge of the phenotypic spectrum of MWS and its correlation with the genotype will improve its detection rate and the prediction of its features, thus improving patient care.GENETICS in MEDICINE advance online publication, 4 January 2018; doi:10.1038/gim.2017.221

Phenotype and genotype of 87 patients with Mowat–Wilson syndrome and recommendations for care

Purpose: Mowat–Wilson syndrome (MWS) is a rare intellectual disability/multiple congenital anomalies syndrome caused by heterozygous mutation of the ZEB2 gene. It is generally underestimated because its rarity and phenotypic variability sometimes make it difficult to recognize. Here, we aimed to better delineate the phenotype, natural history, and genotype–phenotype correlations of MWS. Methods: In a collaborative study, we analyzed clinical data for 87 patients with molecularly confirmed diagnosis. We described the prevalence of all clinical aspects, including attainment of neurodevelopmental milestones, and compared the data with the various types of underlying ZEB2 pathogenic variations. Results: All anthropometric, somatic, and behavioral features reported here outline a variable but highly consistent phenotype. By presenting the most comprehensive evaluati

Languages with mismatches and an application to approximate indexing

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 represents the set of all factors of L(S,k,r) having length equal to R(S,k,r). For each word x ?L(S, k, r) this data structure allows us to find the list occ(x) of all occurrences of the word x in a text S up to k mismatches every r symbols in time proportional to |x| + |occ(x)|

OCCUPATIONAL EMBEDDEDNESS AND INTER-ORGANIZATIONAL MOBILITY: AN EXPLORATORY STUDY IN A CREATIVE INDUSTRY

Extant research highlights two major categories of predictors of job mobility: one emphasizes structural/macro-economic factors such as economic conditions or industry differences; the second one focuses on individual attitudes and decisional factors. This article aims at contributing to extant literature by using the recently introduced construct of occupational embeddedness to predict individual intention to change organization. More specifically, this study hypothesizes that the intention to leave the present organizational setting may be affected not only by the perceived ease of movement in the labor market that is reflected by perceived job alternatives, and by attitudinal factors, such as the individual predisposition toward protean and boundaryless career, but also by the level in which individuals are enmeshed in their profession. In order to test our research hypothesis, we carried out an exploratory study investigating an occupational community operating in a film industry district. More specifically, we conducted a survey on 106 creative professionals who work for companies of special effects in Soho, London. Results confirm the eminent role played by boundaryless career attitude in predicting intention to change organization. However, they also show that in occupational communities in which there is a great cultural acceptance of inter-organizational mobility, intention to leave present organizational setting is also influenced by the individual level of embeddedness in the occupation

Novel Combinatorial and Information Theoretic Alignment Free Distances for Biological Data Mining

Among the plethora of alignment-free methods for comparing biological sequences, there are some that we have perceived as representative of the novel techniques that have been devised in the past few years and as being of a fundamental nature and of broad interest and applicability, ranging from combinatorics to information theory. In this chapter, we review these alignment free methods, by presenting both their mathematical definitions and the experiments in which they are involved in

Sturmian Graphs and a conjecture of Moser

In this paper we define Sturmian graphs and we prove that all of them have a "counting" property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of CDAWGs of central Sturmian words. We show also that, analogously to the case of Sturmian words, these graphs converge to infinite ones