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

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

Epigenetic regulation of asthma and allergic disease

Epigenetics of asthma and allergic disease is a field that has expanded greatly in the last decade. Previously thought only in terms of cell differentiation, it is now evident the epigenetics regulate many processes. With T cell activation, commitment toward an allergic phenotype is tightly regulated by DNA methylation and histone modifications at the Th2 locus control region. When normal epigenetic control is disturbed, either experimentally or by environmental exposures, Th1/Th2 balance can be affected. Epigenetic marks are not only transferred to daughter cells with cell replication but they can also be inherited through generations. In animal models, with constant environmental pressure, epigenetically determined phenotypes are amplified through generations and can last up to 2 generations after the environment is back to normal. In this review on the epigenetic regulation of asthma and allergic diseases we review basic epigenetic mechanisms and discuss the epigenetic control of Th2 cells. We then cover the transgenerational inheritance model of epigenetic traits and discuss how this could relate the amplification of asthma and allergic disease prevalence and severity through the last decades. Finally, we discuss recent epigenetic association studies for allergic phenotypes and related environmental risk factors as well as potential underlying mechanisms for these associations

Tree species, crown cover, and age as determinants of the vertical distribution of airborne LiDAR returns

Light detection and ranging (LiDAR) provides information on the vertical structure of forest stands enabling detailed and extensive ecosystem study. The vertical structure is often summarized by scalar features and data-reduction techniques that limit the interpretation of results. Instead, we quantified the influence of three variables, species, crown cover, and age, on the vertical distribution of airborne LiDAR returns from forest stands. We studied 5,428 regular, even-aged stands in Quebec (Canada) with five dominant species: balsam fir (Abies balsamea (L.) Mill.), paper birch (Betula papyrifera Marsh), black spruce (Picea mariana (Mill.) BSP), white spruce (Picea glauca Moench) and aspen (Populus tremuloides Michx.). We modeled the vertical distribution against the three variables using a functional general linear model and a novel nonparametric graphical test of significance. Results indicate that LiDAR returns from aspen stands had the most uniform vertical distribution. Balsam fir and white birch distributions were similar and centered at around 50% of the stand height, and black spruce and white spruce distributions were skewed to below 30% of stand height (p<0.001). Increased crown cover concentrated the distributions around 50% of stand height. Increasing age gradually shifted the distributions higher in the stand for stands younger than 70-years, before plateauing and slowly declining at 90-120 years. Results suggest that the vertical distributions of LiDAR returns depend on the three variables studied

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

Dynamical Formation of Millisecond Pulsars in Globular Clusters

The cumulative luminosity distribution functions (CLFs) of radio millisecond pulsars (MSPs) in globular clusters (GCs) and in the Galactic field at a frequency of 1.4 GHz have been examined. Assuming a functional form, $N \propto L^q$ where $N$ is the number of MSPs and $L$ is the luminosity at 1.4 GHz, it is found that the CLFs significantly differ with a steeper slope, $q=-0.83 \pm 0.05$, in GCs than in the Galactic field ($q=-0.48 \pm 0.04$), suggesting a different formation or evolutionary history of MSPs in these two regions of the Galaxy. To probe the production mechanism of MSPs in clusters, a search of the possible relationships between the MSP population and cluster properties was carried out. The results of an investigation of 9 GCs indicate positive correlations between the MSP population and the stellar encounter rate and metallicity. This provides additional evidence suggesting that stellar dynamical interactions are important in the formation of the MSP population in GCs.Comment: 18 pages, 3 figures, 4 tables, accepted for publication in Ap