Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells

After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.Comment: 44 figure

From modular invariants to graphs: the modular splitting method

28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determined.International audienceWe start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators, and, as a by-product, recover the known graphs E4(SU4), E6(SU4) and E8(SU4) describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoids.Comment: 33 pages, 3 color figure

Epidemiology and cost of herpes zoster and postherpetic neuralgia among patients treated in primary care centres in the valencian community of Spain

<p>Abstract</p> <p>Background</p> <p>Data on the epidemiology and costs related to herpes zoster (HZ) and postherpetic neuralgia (PHN) in Spain are scarce; therefore, studies are needed to evaluate the epidemiological and economic impact of HZ and its most common complication, PHN. The present study aimed to estimate the clinical and economic burden of HZ and PHN in Valencia (Spain).</p> <p>Methods</p> <p>We prospectively analyzed the burden of HZ and PHN and their attributable costs in patients from 25 general practices in the Autonomous Community of Valencia serving 36,030 persons aged > 14 years. All patients with a clinical diagnosis of HZ who attended these centers between December 1^st2006 and November 30^th2007 were asked to participate. Patients included were followed for 1 year.</p> <p>Results</p> <p>Of the 130 cases of HZ followed up, continued pain was experienced by 47.6% (95% confidence interval (CI) = 35.6-56.7%) at 1 month after rash onset, by 14.5% (95% CI = 7.8-1.2%) at 3 months, by 9.0% (95% CI = 3.7-14.3%) at 6 months, and by 5.9% (95% CI = 1.5-10.3%) at 12 months. The percentage of patients with PHN increased with age, from 21.4% (95% CI = 8.3-40) in patients < 50 years to 59.2% (95% CI = 44.4-74) in patients ≥ 70 years. The estimated total cost for the 130 HZ cases during the follow-up period was €49,160 ($67,349). Mean cost per patient was €378 (range 53-2,830) ($517, range 73-3,877).</p> <p>Conclusions</p> <p>This study shows that PHN is a relatively common complication of HZ and that both conditions combined give rise to a significant clinical and economic burden for patients and providers.</p

L'algèbre des symétries quantiques d'Ocneanu et la classification des systèmes conformes à 2D

Thèse effectuée en cotutelle avec l'Universidade Federal do Rio de Janeiro. Disponible aussi en portuguais.The partition functions of a 2D conformal system - the modular invariant one or the generalized ones, coming from the introduction of defect lines - are expressed in terms of a set of coefficients that have the particularity to form nimreps of certain algebras. These coefficients define the various structure maps of a new class of Hopf Algebras, called Weak Hopf Algebras, and can be encoded in a set of graphs. The aim of chapter 1 is a presentation of the actual knowledge on this subject. In chapter 2 the Weak Hopf Algebra together with its structures is introduced, in particular the Ocneanu algebra of quantum symmetries, that play a key role in the study of 2d conformal systems. We analyze in details these structures for the A3 diagram, associated to the affine su(2) conformal system. In chapter 3, we present a realization of the Ocneanu algebra of quantum symmetries, constructed as a quotient of the tensor square of a graph algebra (ADE graph for the affine (2) model). This realization allows obtaining a very simple algorithm for the determination of the partition functions associated with the conformal model. Our construction can be naturally generalized to the affine su(n) cases, with n > 2, where few results were known. All the cases related of su(2)-type as well as three particular examples of su(3)-type are explicitly treated in chapter 4.Cette thèse étudie la classification des théories conformes à 2d à l'aide de symétries quantiques de diagrammes. Les fonctions de partition d'un système conforme - l'invariante modulaire ou celles provenant de l'introduction de lignes de défauts - s'expriment en fonction d'un ensemble de coefficients qui forment des nimreps de certaines algèbres. Ces coefficients définissent les diverses structures d'une classe d'algèbres de Hopf, dites faibles, et peuvent être codés par un ensemble de graphes. Le chapitre 1 présente les connaissances actuelles sur ce sujet. Dans le chapitre 2 sont introduites l'algèbre de Hopf faible et ses structures, notamment l'algèbre des symétries quantiques d'Ocneanu, qui joue un rôle important dans l'étude des systèmes conformes à 2d. Nous analysons en détails ces structures pour le diagramme A3 du modèle affin su(2). Le chapitre 3 est dédié à la présentation d'une réalisation de l'algèbre des symétries quantiques d'Ocneanu, construite comme un quotient du carré tensoriel de l'algèbre d'un graphe G (de type ADE pour le modèle affin su(2)). Cette réalisation permet d'obtenir un algorithme simple permettant le calcul des fonctions de partition du modèle conforme associé. Notre construction se prête naturellement à une généralisation aux cas affins su(n), pour n > 2, pour lesquels peu de résultats étaient connus. Dans le chapitre 4, nous traitons explicitement tous les cas du type su(2) ainsi que trois exemples choisis du type su(3)

L'algèbre des symétries quantiques d'Ocneanu et la classification des systèmes conformes à 2D

Thèse effectuée en cotutelle avec la UFRJ - Universidade Federal do Rio de Janeiro. Disponible aussi en portuguais.The partition functions of a 2D conformal system - the modular invariant one or the generalized ones, coming from the introduction of defect lines - are expressed in terms of a set of coefficients that have the particularity to form nimreps of certain algebras. These coefficients define the various structure maps of a new class of Hopf Algebras, called Weak Hopf Algebras, and can be encoded in a set of graphs. The aim of chapter 1 is a presentation of the actual knowledge on this subject. In chapter 2 the Weak Hopf Algebra together with its structures is introduced, in particular the Ocneanu algebra of quantum symmetries, that play a key role in the study of 2d conformal systems. We analyze in details these structures for the A3 diagram, associated to the affine su(2) conformal system. In chapter 3, we present a realization of the Ocneanu algebra of quantum symmetries, constructed as a quotient of the tensor square of a graph algebra (ADE graph for the affine (2) model). This realization allows obtaining a very simple algorithm for the determination of the partition functions associated with the conformal model. Our construction can be naturally generalized to the affine su(n) cases, with n > 2, where few results were known. All the cases related of su(2)-type as well as three particular examples of su(3)-type are explicitly treated in chapter 4

L'Algèbre des symétries quantiques d'Ocneanu et la classification des systèmes conformes à 2D

Cette thèse présente la classification des théories conformes à deux dimensions à l'aide de symétries quantiques de diagrammes. Les fonctions de partition d'un système conforme s'écrivent en fonction de coefficients pouvant être codés par des graphes, et qui proviennent des structures d'une algèbre de Hopf faible. Le chapitre 1 présente les connaissances actuelles sur ce sujet. Dans le chapitre 2 sont introduites les structures de l'algèbre de Hopf faible, notamment l'algèbre des symétries quantiques d'Ocneanu. L'exemple du graphe A3 est traité en détails. Dans le chapitre 3 est présentée une réalisation de l'algèbre des symétries quantiques, construite comme un quotient du carré tensoriel de l'algèbre d'un graphe G (de type ADE pour le modèle su (2)). Cette réalisation donne un algorithme simple pour le calcul des fonctions de partition du modèle conforme associé. Dans le chapitre 4, nous traitons explicitement tous les cas du type su (2) et trois exemples du type su (3).AIX-MARSEILLE1-BU Sci.St Charles (130552104) / SudocSudocFranceF