Finite W Algebras and Intermediate Statistics

New realizations of finite W algebras are constructed by relaxing the usual constraint conditions. Then, finite W algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well-adapted for a possible generalization of the anyon statistics.Comment: 16 pp., Latex, Preprint ENSLAPP-489/9

The Stellar Composition of the Star Formation Region CMa R1. II. Spectroscopic and Photometric Observations of 9 Young Stars

We present new high and low resolution spectroscopic and photometric data of nine members of the young association CMa R1. All the stars have circumstellar dust at some distance as could be expected from their association with reflection nebulosity. Four stars (HD 52721, HD 53367, LkHalpha 220 and LkHalpha 218) show Halpha emission and we argue that they are Herbig Be stars with discs. Our photometric and spectroscopic observations on these stars reveal new characteristics of their variability. We present first interpretations of the variability of HD 52721, HD 53367 and the two LkHalpha stars in terms of a partially eclipsing binary, a magnetic activity cycle and circumstellar dust variations, respectively. The remaining five stars show no clear indications of Halpha emission in their spectra, although their spectral types and ages are comparable with those of HD 52721 and HD 53367. This indicates that the presence of a disc around a star in CMa R1 may depend on the environment of the star. In particular we find that all Halpha emission stars are located at or outside the arc-shaped border of the H II region, which suggests that the stars inside the arc have lost their discs through evaporation by UV photons from nearby O stars, or from the nearby (< 25 pc) supernova, about 1 Myr ago.Comment: 17 pages, 13 figures, accepted by MNRA

Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation

A complete set of commuting observables for the Calogero-Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the co-algebra invariance of the model; with the proper technical modifications this procedure can be applied to the $q-$deformed version of the model, which is then also exactly solved.Comment: 20 pages Late

Differential deposition of fibronectin by asthmatic bronchial epithelial cells

© 2015 the American Physiological Society. Altered ECM protein deposition is a feature in asthmatic airways. Fibronectin (Fn), an ECM protein produced by human bronchial epithelial cells (HBECs), is increased in asthmatic airways. This study investigated the regulation of Fn production in asthmatic or nonasthmatic HBECs and whether Fn modulated HBEC proliferation and inflammatory mediator secretion. The signaling pathways underlying transforming growth factor (TGF)-β1-regulated Fn production were examined using specific inhibitors for ERK, JNK, p38 MAPK, phosphatidylinositol 3 kinase, and activin-like kinase 5 (ALK5). Asthmatic HBECs deposited higher levels of Fn in the ECM than nonasthmatic cells under basal conditions, whereas cells from the two groups had similar levels of Fn mRNA and soluble Fn. TGF-β1 increased mRNA levels and ECM and soluble forms of Fn but decreased cell proliferation in both cells. The rate of increase in Fn mRNA was higher in nonasthmatic cells. However, the excessive amounts of ECM Fn deposited by asthmatic cells after TGF-β1 stimulation persisted compared with nonasthmatic cells. Inhibition of ALK5 completely prevented TGF- β1-induced Fn deposition. Importantly, ECM Fn increased HBEC proliferation and IL-6 release, decreased PGE2 secretion, but had no effect on VEGF release. Soluble Fn had no effect on cell proliferation and inflammatory mediator release. Asthmatic HBECs are intrinsically primed to produce more ECM Fn, which when deposited into the ECM, is capable of driving remodeling and inflammation. The increased airway Fn may be one of the key driving factors in the persistence of asthma and represents a novel, therapeutic target

On the Cohomology of the Noncritical WW-string

We investigate the cohomology structure of a general noncritical $W_N$-string. We do this by introducing a new basis in the Hilbert space in which the BRST operator splits into a ``nested'' sum of nilpotent BRST operators. We give explicit details for the case $N=3$. In that case the BRST operator $Q$ can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: $Q=Q_0+Q_1$. We argue that if one chooses for the Liouville sector a $(p,q)$ $W_3$ minimal model then the cohomology of the $Q_1$ operator is closely related to a $(p,q)$ Virasoro minimal model. In particular, the special case of a (4,3) unitary $W_3$ minimal model with central charge $c=0$ leads to a $c=1/2$ Ising model in the $Q_1$ cohomology. Despite all this, noncritical $W_3$ strings are not identical to noncritical Virasoro strings.Comment: 38 pages, UG-7/93, ITP-SB-93-7

Representation theory of finite W algebras

In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.Comment: 62 pages, THU-92/32, ITFA-28-9

A quantitative proteomic approach to identify significantly altered protein networks in the serum of patients with lymphangioleiomyomatosis (LAM)

Lymphangioleiomyomatosis (LAM) is a rare and progressive cystic lung condition affecting approximately 3.4-7.5/million women, with an average lag time between symptom onset and diagnosis of upwards of 4 years. The aim of this work was to identify altered proteins in LAM serum which may be potential biomarkers of disease. Serum from LAM patient volunteers and healthy control volunteers were pooled and analysis carried out using quantitative 4-plex iTRAQ technology. Differentially expressed proteins were validated using ELISAs and pathway analysis was carried out using Ingenuity Pathway Analysis. Fourteen proteins were differentially expressed in LAM serum compared to control serum (p<0.05). Further screening validated the observed differences in extracellular matrix remodelling proteins including fibronectin (30% decrease in LAM, p = 0.03), von Willebrand Factor (40% reduction in LAM, p = 0.03) and Kallikrein III (25% increase in LAM, p = 0.03). Pathway networks elucidated the relationships between the ECM and cell trafficking in LAM. This study was the first to highlight an imbalance in networks important for remodelling in LAM, providing a set of novel potential biomarkers. These understandings may lead to a new effective treatment for LAM in the future. © 2014 Banville et al

The Stellar Composition of the Star Formation Region CMa R1 -- III. A new outburst of the Be star component in Z CMa

We report on a recent event in which, after more than a decade of slowly fading, the visual brightness of the massive young binary Z CMa suddenly started to rise by about 1 magnitude in December 1999, followed by a rapid decline to its previous brightness over the next six months. This behaviour is similar to that exhibited by this system around its eruption in February 1987. A comparison of the intrinsic luminosities of the system with recent evolutionary calculations shows that Z CMa may consist of a 16 M_sun B0 IIIe primary star and a ~ 3 M_sun FUOr secondary with a common age of ~ 3 x 10^5 yr. We also compare new high-resolution spectra obtained in Jan. and Feb. 2000, during the recent rise in brightness, with archive data from 1991 and 1996. The spectra are rich in emission lines, which originate from the envelope of the early B-type primary star. The strength of these emission lines increased strongly with the brightness of Z CMa. We interpret the collected spectral data in terms of an accretion disc with atmosphere around the Herbig B0e component of Z CMa, which has expanded during the outbursts of 1987 and 2000. A high resolution profile of the 6300 A [O I] emission line, obtained by us in March 2002 shows an increase in flux and a prominent blue shoulder to the feature extending to ~ -700 km/s, which was much fainter in the pre-outburst spectra. We propose that this change in profile is a result of a strong change in the collimation of a jet, as a result of the outburst at the start of this century.Comment: 22 pages, 12 figures, accepted for publication in MNRA

The Kazhdan-Lusztig conjecture for finite W-algebras

We study the representation theory of finite W-algebras. After introducing parabolic subalgebras to describe the structure of W-algebras, we define the Verma modules and give a conjecture for the Kac determinant. This allows us to find the completely degenerate representations of the finite W-algebras. To extract the irreducible representations we analyse the structure of singular and subsingular vectors, and find that for W-algebras, in general the maximal submodule of a Verma module is not generated by singular vectors only. Surprisingly, the role of the (sub)singular vectors can be encapsulated in terms of a `dual' analogue of the Kazhdan-Lusztig theorem for simple Lie algebras. These involve dual relative Kazhdan-Lusztig polynomials. We support our conjectures with some examples, and briefly discuss applications and the generalisation to infinite W-algebras.Comment: 11 page

Three dimensional quantum algebras: a Cartan-like point of view

A perturbative quantization procedure for Lie bialgebras is introduced and used to classify all three dimensional complex quantum algebras compatible with a given coproduct. The role of elements of the quantum universal enveloping algebra that, analogously to generators in Lie algebras, have a distinguished type of coproduct is discussed, and the relevance of a symmetrical basis in the universal enveloping algebra stressed. New quantizations of three dimensional solvable algebras, relevant for possible physical applications for their simplicity, are obtained and all already known related results recovered. Our results give a quantization of all existing three dimensional Lie algebras and reproduce, in the classical limit, the most relevant sector of the complete classification for real three dimensional Lie bialgebra structures given by X. Gomez in J. Math. Phys. Vol. 41. (2000) 4939.Comment: LaTeX, 15 page