The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also discussed on the basis of the analytical solution of the wave kinetic equation specific to Gaussian beams of electromagnetic waves propagating in a ``lens-like'' medium for which the complex geometrical optics solution is already available.Comment: Extended version comprising two new section

Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0}$on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.Comment: 8 page

Non-commutative integrable systems on bb-symplectic manifolds

In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a $b$-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure

Editorial ISTRY Special Issue

Editorial by Dr Guillemin, Head of the Neuroinflammation Group, University of New South Wales, Department of Pharmacology, Sydney, NSW, Australia

Cohomology of GKM Fiber Bundles

The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and derive a graph theoretical version of the Leray-Hirsch theorem. Then we apply this result to the equivariant cohomology theory of flag varieties.Comment: The paper has been accepted by the Journal of Algebraic Combinatorics. The final publication is available at springerlink.co

Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras

We describe the group of continuous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify F-forms of these superalgebras over any field F of characteristic zero.Comment: 24 page

Kynurenine Pathway Metabolites in Humans: Disease and Healthy States

Tryptophan is an essential amino acid that can be metabolised through different pathways, a major route being the kynurenine pathway. The first enzyme of the pathway, indoleamine-2,3-dioxygenase, is strongly stimulated by inflammatory molecules, particularly interferon gamma. Thus, the kynurenine pathway is often systematically up-regulated when the immune response is activated. The biological significance is that 1) the depletion of tryptophan and generation of kynurenines play a key modulatory role in the immune response; and 2) some of the kynurenines, such as quinolinic acid, 3-hydroxykynurenine and kynurenic acid, are neuroactive. The kynurenine pathway has been demonstrated to be involved in many diseases and disorders, including Alzheimer’s disease, amyotrophic lateral sclerosis, Huntington’s disease, AIDS dementia complex, malaria, cancer, depression and schizophrenia, where imbalances in tryptophan and kynurenines have been found. This review compiles most of these studies and provides an overview of how the kynurenine pathway might be contributing to disease development, and the concentrations of tryptophan and kynurenines in the serum, cerebrospinal fluid and brain tissues in control and patient subjects

Searching for Trans Ethyl Methyl Ether in Orion KL

We report on the tentative detection of $trans$ Ethyl Methyl Ether (tEME), $t-CH_3CH_2OCH_3$, through the identification of a large number of rotational lines from each one of the spin states of the molecule towards Orion KL. We also search for $gauche$-$trans$-n-propanol, $Gt-n-CH_3CH_2CH_2OH$, an isomer of tEME in the same source. We have identified lines of both species in the IRAM 30m line survey and in the ALMA Science Verification data. We have obtained ALMA maps to establish the spatial distribution of these species. Whereas tEME mainly arises from the compact ridge component of Orion, Gt-n-propanol appears at the emission peak of ethanol (south hot core). The derived column densities of these species at the location of their emission peaks are $\leq(4.0\pm0.8)\times10^{15} cm^{-2}$ and $\leq(1.0\pm0.2)\times10^{15} cm^{-2}$ for tEME and Gt-n-propanol, respectively. The rotational temperature is $\sim100 K$ for both molecules. We also provide maps of $CH_3OCOH$, $CH_3CH_2OCOH$, $CH_3OCH_3$, $CH_3OH$, and $CH_3CH_2OH$ to compare the distribution of these organic saturated O-bearing species containing methyl and ethyl groups in this region. Abundance ratios of related species and upper limits to the abundances of non-detected ethers are provided. We derive an abundance ratio $N(CH_3OCH_3)/N(tEME)\geq150$ in the compact ridge of Orion.Comment: Accepted in A&A Letter

Exposure to carcinogenic polycyclic aromatic compounds and health risk assessment for diesel-exhaust exposed workers

Objectives: Workers' exposure to diesel exhaust in a bus depot, a truck repair workshop and an underground tunnel was determined by the measuring of elemental carbon (EC) and 15 carcinogenic polycyclic aromatic compounds (PACs) proposed by the US Department of Health and Human Services/National Toxicology Program (NTP). Based on these concentration data, the genotoxic PAC contribution to the diesel-exhaust particle (DEP) lung-cancer risk was calculated. Method: Respirable particulate matter was collected during the summer and winter of 2001 (except for in the underground situation) and analysed by coulometry for EC and by GC-MS methods for PACs. The use of potency equivalence factors (PEFs) allowed the studied PAC concentrations to be expressed as benzo[a]pyrene equivalents (B[a]Peq). We then calculated the lung-cancer risk due to PACs and DEPs by multiplying the B[a]Peq and EC concentrations by the corresponding unit risk factor. The ratio of these two risks values has been considered as an estimate of the genotoxic contribution to the DEP cancer risk. Results: For the bus depot and truck repair workshop, exposure to EC and PACs has been shown to increase by three to six times and ten times, respectively, during winter compared to summer. This increase has been attributed mainly to a decrease in ventilation during the cold. With the PEF approach, the B[a]Peq concentration is five-times higher than if only benzo[a]pyrene (B[a]P) is considered. Dibenzopyrenes contribute an important part to this increase. A simple calculation based on unit risk factors indicates that the studied PAC contribution to the total lung-cancer risk attributed to DEPs is in the range of 3-13%. Conclusions: The 15 NTP PACs represent a small but non-negligible part of lung-cancer risk with regard to diesel exposure. From this point of view, the dibenzopyrene family are important compounds to be considere