Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

Quasi-particles in Fractional Quantum Hall Effect Edge Theories

We propose a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. For the edge of a Laughlin state with filling fraction \nu=1/m, our fundamental quasi-particles are edge electrons of charge -e and edge quasi-holes of charge +e/m. These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a kinetic equation for charge transport between a \nu=1/m fractional quantum Hall edge and a normal metal. We also analyze alternative `Boltzmann' equations that are directly based on the exclusion statistics properties of edge quasi-particles. Generalizations to more general filling fractions (Jain series) are briefly discussed.Comment: 20 pages, 2 eps figures, revtex, references updated, Phys. Rev. B in pres

Exact perturbative solution of the Kondo problem

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.Comment: 4 pages in revtex two-colum

Reduction of myocardial infarct size by neutrophil depletion: Effect of duration of occlusion

Experiments were performed in the dog to examine the effects of neutropenia on ultimate infarct size resulting from short (90 minutes) or prolonged (4 hours) circumflex coronary artery occlusion. Sheep antiserum to canine neutrophils was used to produce neutropenia. Control animals received nonimmune serum. Neutrophil infiltration into myocardial infarcts was examined using histopathologic techniques and a semiquantitative scoring system. In 90-minute occlusions with 24-hour reperfusion, neutropenia was associated with the development of significantly smaller infarcts: normopenic group, 43.2% +/- 3.3% (n = 7) vs. neutropenic group, 26.6% +/- 3.7% (n = 10) of the area at risk, +/- SEM. However, in 4-hour occlusion with 6-hour reperfusion experiments, the tendency of neutrophil depletion to reduce infarct size did not reach statistical significance (46.4% +/- 7.2% vs. 31.5% +/- 6.0% of the area at risk, normopenic vs. neutropenic) despite differences in neutrophil infiltration into the reperfused region. The observed differences in ultimate infarct size could not be attributed to differences in myocardial oxygen consumption. The results suggest that a significant amount of myocardial infarction induced by a limited duration of coronary artery occlusion followed by reperfusion is neutrophil dependent and appears to be less important in determining the fate of myocardium subjected to more prolonged periods of ischemia followed by reperfusion.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26030/1/0000103.pd

Zero-field spin-splitting and spin lifetime in n-InSb/In1-xAlxSb asymmetric quantum well heterostructures

The spin-orbit (SO) coupling parameters for lowest conduction subband due to structural (SIA) and bulk (BIA) inversion asymmetry are calculated for a range of carrier densities in [001]-grown delta-doped n-type InSb/In1-xAlxSb asymmetric quantum wells using the established 8 band k.p formalism [PRB 59,8 R5312 (1999)]. We present calculations for conditions of zero bias at 10 K. It is shown that both the SIA and BIA parameters scale approximately linearly with carrier density, and exhibit a marked dependence on well width when alloy composition is adjusted to allow maximum upper barrier height for a given well width. In contrast to other material systems the BIA contribution to spin splitting is found to be of significant and comparable value to the SIA mechanism in these structures. We calculate the spin lifetime for spins oriented along [11-0] based on D'yakonov-Perel mechanism using both the theory of Averkiev et al. [J. Phys.:Condens. Matter 14 (2002)] and also the rate of precession of spins about the effective magnetic field, taking into account all three SO couplings, showing good agreement.Spin lifeime for this direction is largest in the narrow wells over the range of moderate carrier densities considered, which is attributed to the reduced magnitude of the k-cubic BIA parameter in narrow wells. The inherently large BIA induced SO coupling in these systems is shown to have considerable effect on the spin lifetime, which exhibits significant reduction in the maximum spin lifetime compared to previous studies which consider systems with relatively weak BIA induced SO coupling. The relaxation rate of spins oriented in the [001] direction is dominated by the k-linear SIA and BIA coupling parameters and at least an order of magnitude greater than in the [11-0] direction.Comment: 18 pages 12 figure

Solving 1d plasmas and 2d boundary problems using Jack polynomials and functional relations

The general one-dimensional ``log-sine'' gas is defined by restricting the positive and negative charges of a two-dimensional Coulomb gas to live on a circle. Depending on charge constraints, this problem is equivalent to different boundary field theories. We study the electrically neutral case, which is equivalent to a two-dimensional free boson with an impurity cosine potential. We use two different methods: a perturbative one based on Jack symmetric functions, and a non-perturbative one based on the thermodynamic Bethe ansatz and functional relations. The first method allows us to compute explicitly all coefficients in the virial expansion of the free energy and the experimentally-measurable conductance. Some results for correlation functions are also presented. The second method provides in particular a surprising fluctuation-dissipation relation between the free energy and the conductance.Comment: 19 page

The structure of the tetrasialoganglioside from human brain

Autosomal dominant retinal vasculopathy with cerebral leukodystrophy is a microvascular endotheliopathy with middle- age onset. In nine families, we identified heterozygous C- terminal frameshift mutations in TREX1, which encodes a 3'-5' exonuclease. These truncated proteins retain exonuclease activity but lose normal perinuclear localization. These data have implications for the maintenance of vascular integrity in the degenerative cerebral microangiopathies leading to stroke and dementias

A call for transparent reporting to optimize the predictive value of preclinical research

The US National Institute of Neurological Disorders and Stroke convened major stakeholders in June 2012 to discuss how to improve the methodological reporting of animal studies in grant applications and publications. The main workshop recommendation is that at a minimum studies should report on sample-size estimation, whether and how animals were randomized, whether investigators were blind to the treatment, and the handling of data. We recognize that achieving a meaningful improvement in the quality of reporting will require a concerted effort by investigators, reviewers, funding agencies and journal editors. Requiring better reporting of animal studies will raise awareness of the importance of rigorous study design to accelerate scientific progress