Quadratic Cyclic Sequences

We explore relations between cyclic sequences determined by a quadratic difference relation, cyclotomic polynomials, Eulerian digraphs and walks in the plane. These walks correspond to closed paths for which at each step one must turn either left or right through a fixed angle. In the case when this angle is $2 \pi /n$, then non-symmetric phenomena occurs for $n\geq 12$. Examples arise from algebraic numbers of modulus one which are not $n$'th roots of unity

Se raconter par l’autre

Rétrospective est une « exposition conçue comme une chorégraphie d’actions », selon les mots de Xavier le Roy. Elle prend place au sein d’espaces muséaux et a déjà été accueillie à Barcelone, Rennes, Salvador, Hambourg, Rio et Paris. Contrepoint aux attentes d’un retour sur la vie d’un artiste, l’initiative détourne la rigidité et la monumentalité d’une œuvre, lui préférant le « recyclage » de fragments des huit solo du chorégraphe créés entre 1994 et 2010, transmis à une vingtaine de danseur..

Bronchiolitis Admissions in a Lebanese Tertiary Medical Center: A 10 Years' Experience

Bronchiolitis and more specifically respiratory syncytial virus (RSV) bronchiolitis is a leading cause of global childhood morbidity and mortality. Despite the previous identification of possible risk factors associated with the severity of bronchiolitis, the data from Lebanon remains limited. We described the burden of bronchiolitis hospitalizations in children under 5 years of age in a tertiary care center in Lebanon from October 2004 to October 2014 and identified the risk factors associated with severe bronchiolitis. This was a retrospective cohort study conducted at the American University of Beirut Medical Center. Records of children younger than 5 years of age admitted with a diagnosis of bronchiolitis were reviewed. More than half the patients were RSV positive. RSV bronchiolitis was found to be significantly associated with longer hospital stay compared to children with non-RSV bronchiolitis (P = 0.007). Children exposed to smoking had an increased risk for longer hospital stay (P = 0.002) and were more likely to require ICU admission (P < 0.001) and supplemental oxygen (P = 0.045). Congenital heart disease was found to be a significant risk factor for severe bronchiolitis (P < 0.005).Conclusion: Patients with RSV bronchiolitis had a longer hospital stay compared to patients with non-RSV bronchiolitis. Exposure to smoking was associated with a more severe and complicated RSV infection. Congenital heart disease was the only risk factor significantly associated with all markers of bronchiolitis disease severity

Combinatorial and geometric cycles

Le travail de cette thèse se situe dans les domaines de la théorie combinatoire des graphes, la combinatoire algébrique et la géométrie discrète. D'un part, il concerne l'énumération des chemins et cycles Hamiltoniens de type donné dans un tournoi ; de l'autre part, il étudie des suites numériques vérifiant une équation à différence quadratique. Parmi les résultats obtenus dans la première partie, on trouve : une égalité entre le nombre des chemins (resp. cycles) Hamiltoniens d’un type donné dans un tournoi et dans son complément; une expression du nombre de chemins Hamiltoniens d’un type donné pour un tournoi transitif en termes d'une fonction récursive F appelée « path-function »; la construction d'un algorithme pour le calcul de F. L'objet fondamental dans la deuxième partie est un graphe cyclique muni d'une solution d'une équation à différence quadratique. Un paramètre de cette équation distingue les solutions réelles et les solutions complexes. Une correspondance entre les solutions réelles et une classe de polynômes à coefficients entiers positifs est établie. Pour compléter la correspondance, les digraphes Eulériens à un pas interviennent. Une solution complexe détermine une marche fermée dans le plan pour laquelle à chaque pas on tourne à gauche ou à droite par un angle constant (l'angle tournant). Cette fois-ci les polynômes cyclotomiques jouent un rôle important. La caractérisation des polynômes qui déterminent de telles suites est un problème qu’on surmonte afin d'élucider des propriétés géométriques de tels cycles polygonaux. Notamment, lorsque la marche exploite les côtés d'un polygone régulier avec angle extérieur 2π/n, on trouve des phénomènes non anticipés lorsque n≥12.The work in this thesis concerns the combinatorial theory of graphs, algebraic combinatorics and discrete geometry. On one side, it is about enumerating Hamiltonian paths and cycles of a given type in a tournament; On the other side, it studies numerical sequences verifying a quadratic difference equation.Concerning the results of the first part, we find: an equality between the number of Hamiltonians paths (resp. cycles) of a given type, in a tournament and its complement; an expression of the number of Hamiltonian oriented paths of a given type in a transitive tournament in terms of a recursive function F called the « path-function »; and the construction of an algorithm to compute F.In the second part of the work, we study cyclic graphs altogether with a solution to a quadratic difference equation.A parameter of this equation distinguishes real and complex sequences. A correspondence between real solutions and a class of polynomials with positive integer coefficients is established. To complete the correspondence, 1-step Eulerian digraphs interfere. A complex solution determines a closed planar walk in the plane, for which at each step we turn either left or right by a constant angle (the turning angle). This time, cyclotomic polynomials play a major role. Characterizing polynomials that determine such a solution is a problem that we study to the end of finding geometric properties of such polygonal cycles.When the walk exploits the sides of a regular polygon with exterior angle 2 π/n, we find unexpected phenomena when n≥ 12

Cycles combinatoires et géométriques

The work in this thesis concerns the combinatorial theory of graphs, algebraic combinatorics and discrete geometry. On one side, it is about enumerating Hamiltonian paths and cycles of a given type in a tournament; On the other side, it studies numerical sequences verifying a quadratic difference equation.Concerning the results of the first part, we find: an equality between the number of Hamiltonians paths (resp. cycles) of a given type, in a tournament and its complement; an expression of the number of Hamiltonian oriented paths of a given type in a transitive tournament in terms of a recursive function F called the « path-function »; and the construction of an algorithm to compute F.In the second part of the work, we study cyclic graphs altogether with a solution to a quadratic difference equation.A parameter of this equation distinguishes real and complex sequences. A correspondence between real solutions and a class of polynomials with positive integer coefficients is established. To complete the correspondence, 1-step Eulerian digraphs interfere. A complex solution determines a closed planar walk in the plane, for which at each step we turn either left or right by a constant angle (the turning angle). This time, cyclotomic polynomials play a major role. Characterizing polynomials that determine such a solution is a problem that we study to the end of finding geometric properties of such polygonal cycles.When the walk exploits the sides of a regular polygon with exterior angle 2 π/n, we find unexpected phenomena when n≥ 12.Le travail de cette thèse se situe dans les domaines de la théorie combinatoire des graphes, la combinatoire algébrique et la géométrie discrète. D'un part, il concerne l'énumération des chemins et cycles Hamiltoniens de type donné dans un tournoi ; de l'autre part, il étudie des suites numériques vérifiant une équation à différence quadratique. Parmi les résultats obtenus dans la première partie, on trouve : une égalité entre le nombre des chemins (resp. cycles) Hamiltoniens d’un type donné dans un tournoi et dans son complément; une expression du nombre de chemins Hamiltoniens d’un type donné pour un tournoi transitif en termes d'une fonction récursive F appelée « path-function »; la construction d'un algorithme pour le calcul de F. L'objet fondamental dans la deuxième partie est un graphe cyclique muni d'une solution d'une équation à différence quadratique. Un paramètre de cette équation distingue les solutions réelles et les solutions complexes. Une correspondance entre les solutions réelles et une classe de polynômes à coefficients entiers positifs est établie. Pour compléter la correspondance, les digraphes Eulériens à un pas interviennent. Une solution complexe détermine une marche fermée dans le plan pour laquelle à chaque pas on tourne à gauche ou à droite par un angle constant (l'angle tournant). Cette fois-ci les polynômes cyclotomiques jouent un rôle important. La caractérisation des polynômes qui déterminent de telles suites est un problème qu’on surmonte afin d'élucider des propriétés géométriques de tels cycles polygonaux. Notamment, lorsque la marche exploite les côtés d'un polygone régulier avec angle extérieur 2π/n, on trouve des phénomènes non anticipés lorsque n≥12

‘Unknowing’ and mental health system reform in Palestine

In this Think Piece we argue that mental health system reforms are not mainly driven by scientific evidence and international standards, but rather by concrete political constellations, national and international development agendas, local and global socioeconomic contexts, and the interactions between differently positioned actors. We further argue that these forces gain their influence not by being openly discussed, but precisely because they are rendered invisible and turned into what Geissler (2013) calls ‘unknown knowns’. To illustrate these complex processes, we present a case study that examines how mental health system reform processes in the West Bank are shaped by the Israeli occupation, particular political events, and unequal power relations between international and local institutional actors. Furthermore, we present critical reflections by mental health providers related to these processes, and their visions for a more sustainable mental health system. We end with an appeal to aid providers to stop characterising their work with abstract catchphrases such as ‘evidence-based’ or ‘best practice’, and call on them to be transparent about how political, economic, and social contexts shape their work on the ground

Epidemiology, clinical manifestations, and molecular typing of salmonella typhi isolated from patients with typhoid fever in Lebanon

The objective of this study was to examine the epidemiology and the clinical manifestations of typhoid fever as well as the susceptibility and strain relatedness of Salmonella typhi isolates in Lebanon from 2006 to 2007. A total of 120 patients with typhoid fever were initially identified from various areas of the country based on positive culture results for S. typhi from blood, urine, stools, bone marrow and/or positive serology. Clinical, microbiological and molecular analysis was performed on cases with complete data available. These results indicated that drinking water was an unlikely mode of transmission of the infection. Despite increasing reports of antimicrobial resistance among S. typhi isolates, the vast majority of these isolates were susceptible to various antibiotic agents, including ampicillin, cephalosporins, quinolones, and trimethoprim/sulfamethoxazole. Molecular analysis of the isolates revealed a predominance of one single genotype with no variation in distribution across the geographical regions