Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

Intervention de groupe auprès d’enfants présentant des comportements sexuels problématiques : évolution comportementale, affective et sociale

L’objectif de cette étude exploratoire vise à évaluer la participation et l’évolution de 43 enfants présentant des comportements sexuels problématiques ayant participé à un programme d’intervention de groupe. L’évolution des enfants est évaluée à l’aide d’instruments standardisés, administrés avant et après l’intervention de groupe, mesurant diverses dimensions, notamment les comportements sexuels, les problèmes de comportement intériorisés et extériorisés, les habiletés sociales, etc. Les résultats révèlent que dans l’ensemble, toutes variables confondues, les enfants s’améliorent entre le début et la fin de l’intervention de groupe. Plus spécifiquement, les analyses de variance à mesures répétées montrent des améliorations significatives au niveau des comportements sexuels problématiques, des comportements intériorisés et des habiletés sociales. Cette étude suggère que l’intervention de groupe peut s’avérer une modalité d’intervention pouvant répondre aux besoins spécifiques de ces enfants.The purpose of this research is to examine the evolution of children with problematic sexual behaviour following their participation in a group treatment program. The sample was made up of 43 children (33 boys and 10 girls) with an average age of 9 years, 7 months (SD = 1.85) The evolution of the children is measured administering behavioural rating instruments, both before and after the treatment program, on multiple dimensions of problematic sexual behaviour, externalizing and internalizing problems and social skills. The actual level of the children’s participation is documented. The results indicate improvement for a significant portion of the children treated, particularly for those with problematic sexual behaviour, internalizing problems and social skills. This study highlights that treatment group might be a relevant choice of treatment modality.El objetivo de este estudio exploratorio es evaluar la participación y evolución de 43 niños que presentan comportamientos sexuales problemáticos y que participaron en un programa de intervención de grupo. La evolución de los niños se evalúa con ayuda de instrumentos estandarizados, administrados antes y después de la intervención de grupo, que miden diversas dimensiones, específicamente los comportamientos sexuales, los problemas de comportamientos interiorizados y exteriorizados, las habilidades sociales, etc. Los resultados revelan que en conjunto, todas las variables reunidas, los niños se mejoran entre el principio y el fin de la intervención de grupo. Más específicamente, los análisis de variación de medidas repetidas muestran mejoras significativas a nivel de los comportamientos sexuales problemáticos, los comportamientos interiorizados y las habilidades sociales. Este estudio sugiere que la intervención de grupo puede considerarse como una modalidad de intervención que puede responder a las necesidades específicas de estos niños.O objetivo deste estudo exploratório é avaliar a participação e a evolução de 43 crianças, que apresentam comportamentos sexuais problemáticos, que participaram de um programa de intervenção em grupo. A evolução das crianças é avaliada com a ajuda de instrumentos padronizados, administrados antes e após a intervenção em grupo, medindo várias dimensões, principalmente os comportamentos sexuais, os problemas de comportamento interiorizados e exteriorizados, as habilidades sociais, etc. Os resultados revelam que, no geral, sem especificar as variáveis, as crianças demonstram melhoria entre o início e o fim da intervenção em grupo. Mais especificamente, as análises de variação das medidas repetidas mostram melhorias significativas ao nível dos comportamentos sexuais problemáticos, comportamentos interiorizados e habilidades sociais. Este estudo sugere que a intervenção em grupo pode ser uma modalidade de intervenção capaz de responder às necessidades específicas destas crianças

Joint constraints on reionization: a framework for combining the global 21cm signal and the kinetic Sunyaev-Zel'dovich effect

Recent measurements from the CMB and from high-redshift galaxy observations have placed rough constraints on the midpoint and duration of the Epoch of Reionization. Detailed measurements of the ionization history remain elusive, although two proposed probes show great promise for this purpose: the 21cm global signal and the kinetic Sunyaev-Zel'dovich (kSZ) effect. We formally confirm the common assumption that these two probes are highly complementary, with the kSZ being more sensitive to extended ionization histories and the global signal to rapidly evolving ones. We do so by performing a Karhunen-Lo\`{e}ve (KL) transformation, which casts the data in a basis designed to emphasize the information content of each probe. We find that reconstructing the ionization history using both probes gives significantly more precise results than individual constraints, although carefully chosen, physically motivated priors play a crucial part in obtaining a bias-free reconstruction. Additionally, in the KL basis, measurements from one probe can be used to detect the presence of residual systematics in the other, providing a safeguard against systematics that would go undetected when data from each probe is analyzed in isolation. Once detected, the modes contaminated by systematics can be discarded from the data analysis to avoid biases in reconstruction

Mentalization and dissociation in the context of trauma: Implications for child psychopathology

Dissociation is a common reaction subsequent to childhood sexual abuse (CSA) and has been identified as a risk factor for child psychopathology. There is also evidence that mentalization contributes to resilience in the context of abuse. However, at this stage little is known regarding the relationship between mentalization and dissociation, and their respective contributions to psychopathology. The aim of this study was to examine pathways from CSA to depressive symptoms, externalizing behaviour difficulties and sexualized behaviour, through mentalization and dissociation. These pathways were examined in a sample of 168 mother-child dyads including 74 dyads where children (aged 7–12) had histories of sexual abuse. Maternal mentalization was assessed using the Parent Development Interview-Revised and children’s mentalization was assessed using the Child Reflective Functioning Scale. Children completed the Child Depression Inventory and parents completed the Child Dissociative Checklist, the Child Behavior Checklist and the Child Sexual Behavior Inventory. Direct and indirect paths from CSA to child psychopathology via children’s mentalization and dissociation were examined using Mplus. Two distinct paths from abuse to psychopathology were identified. Child mentalization partially mediated the relationship between CSA and depressive symptoms. The effects of CSA on externalizing symptoms and sexualized behaviour difficulties were sequentially mediated through mentalisation and dissociation

Affine su(3) and su(4) fusion multiplicities as polytope volumes

Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for higher-rank fusion multiplicities. The associated threshold levels are also discussed. For any simple Lie algebra we derive an upper bound on the threshold levels using a refined version of the Gepner-Witten depth rule.Comment: 16 pages, LaTe

The optical companion to the binary millisecond pulsar J1824-2452H in the globular cluster M28

We report on the optical identification of the companion star to the eclipsing millisecond pulsar PSR J1824-2452H in the galactic globular cluster M28 (NGC 6626). This star is at only 0.2" from the nominal position of the pulsar and it shows optical variability (~ 0.25 mag) that nicely correlates with the pulsar orbital period. It is located on the blue side of the cluster main sequence, ~1.5 mag fainter than the turn-off point. The observed light curve shows two distinct and asymmetric minima, suggesting that the companion star is suffering tidal distortion from the pulsar. This discovery increases the number of non-degenerate MSP companions optically identified so far in globular clusters (4 out of 7), suggesting that these systems could be a common outcome of the pulsar recycling process, at least in dense environments where they can be originated by exchange interactions.Comment: accepted for publication on ApJ, 17 pages, 5 figure

Chandra X-ray Observations of 12 Millisecond Pulsars in the Globular Cluster M28

We present a Chandra X-ray Observatory investigation of the millisecond pulsars (MSPs) in the globular cluster M28 (NGC 6626). In what is one of the deepest X-ray observations of a globular cluster, we firmly detect seven and possibly detect two of the twelve known M28 pulsars. With the exception of PSRs B1821-24 and J1824-2452H, the detected pulsars have relatively soft spectra, with X-ray luminosities 10^30-31 ergs s^-1 (0.3-8 keV),similar to most "recycled" pulsars in 47 Tucanae and the field of the Galaxy, implying thermal emission from the pulsar magnetic polar caps. We present the most detailed X-ray spectrum to date of the energetic PSR B1821-24. It is well described by a purely non-thermal spectrum with spectral photon index 1.23 and luminosity 1.4x10^33Theta(D/5.5 kpc)^2 ergs s^-1 (0.3-8 keV), where Theta is the fraction of the sky covered by the X-ray emission beam(s). We find no evidence for the previously reported line emission feature around 3.3 keV, most likely as a consequence of improvements in instrument calibration. The X-ray spectrum and pulse profile of PSR B1821--24 suggest that the bulk of unpulsed emission from this pulsar is not of thermal origin, and is likely due to low-level non-thermal magnetospheric radiation, an unresolved pulsar wind nebula, and/or small-angle scattering of the pulsed X-rays by interstellar dust grains. The peculiar binary PSR J1824-2452H shows a relatively hard X-ray spectrum and possible variability at the binary period, indicative of an intrabinary shock formed by interaction between the relativistic pulsar wind and matter from its non-degenerate companion star.Comment: 9 pages, 6 figures. Accepted for publication in the Astophysical Journa