Separation of variables in quasi-potential systems of bi-cofactor form

We perform variable separation in the quasi-potential systems of equations of the form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$ and $\tilde{A}$ are Killing tensors, by embedding these systems into a bi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuis coordinates on the symplectic leaves of one of the Hamiltonian structures of the system. We also present examples of the corresponding separation coordinates in two and three dimensions.Comment: LaTex, 30 pages, to appear in J. Phys. A: Math. Ge

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page

Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey

We test and reject the claim of Segal et al. (1993) that the correlation of redshifts and flux densities in a complete sample of IRAS galaxies favors a quadratic redshift-distance relation over the linear Hubble law. This is done, in effect, by treating the entire galaxy luminosity function as derived from the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance indicator; equivalently, we compare the flux density distribution of galaxies as a function of redshift with predictions under different redshift-distance cosmologies, under the assumption of a universal luminosity function. This method does not assume a uniform distribution of galaxies in space. We find that this test has rather weak discriminatory power, as argued by Petrosian (1993), and the differences between models are not as stark as one might expect a priori. Even so, we find that the Hubble law is indeed more strongly supported by the analysis than is the quadratic redshift-distance relation. We identify a bias in the the Segal et al. determination of the luminosity function, which could lead one to mistakenly favor the quadratic redshift-distance law. We also present several complementary analyses of the density field of the sample; the galaxy density field is found to be close to homogeneous on large scales if the Hubble law is assumed, while this is not the case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros, postscript also available at http://www.astro.princeton.edu/~library/preprints/pop682.ps.g

Type Ia Supernova Explosion Models

Because calibrated light curves of Type Ia supernovae have become a major tool to determine the local expansion rate of the Universe and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most Type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling Type Ia supernovae as well as several of the still open questions are addressed in this review. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics of turbulent nuclear combustion in degenerate stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in pres

Interferon regulatory factor 5 (IRF5) gene variants are associated with multiple sclerosis in three distinct populations

Background: IRF5 is a transcription factor involved both in the type I interferon and the toll-like receptor signalling pathways. Previously, IRF5 has been found to be associated with systemic lupus erythematosus, rheumatoid arthritis and inflammatory bowel diseases. Here we investigated whether polymorphisms in the IRF5 gene would be associated with yet another disease with features of autoimmunity, multiple sclerosis (MS). Methods: We genotyped nine single nucleotide polymorphisms and one insertion-deletion polymorphism in the IRF5 gene in a collection of 2337 patients with MS and 2813 controls from three populations: two case-control cohorts from Spain and Sweden, and a set of MS trio families from Finland. Results: Two single nucleotide polymorphism (SNPs) (rs4728142, rs3807306), and a 5 bp insertion-deletion polymorphism located in the promoter and first intron of the IRF5 gene, showed association signals with values of p<0.001 when the data from all cohorts were combined. The predisposing alleles were present on the same common haplotype in all populations. Using electrophoretic mobility shift assays we observed allele specific differences in protein binding for the SNP rs4728142 and the 5 bp indel, and by a proximity ligation assay we demonstrated increased binding of the transcription factor SP1 to the risk allele of the 5 bp indel. Conclusion: These findings add IRF5 to the short list of genes shown to be associated with MS in more than one population. Our study adds to the evidence that there might be genes or pathways that are common in multiple autoimmune diseases, and that the type I interferon system is likely to be involved in the development of these diseases.Peer Reviewe

Midterm results of the Ross procedure in children: an appraisal of the subannular implantation with interrupted sutures technique

OBJECTIVES: The support of the pulmonary autograft root by the fibromuscular left ventricular outflow tract is emphasized to address the concern related to the dilatation of the pulmonary autograft structures in the paediatric population. METHODS: This retrospective study analyses the outcomes of 75 children who were operated between 1998 and 2012 with the subannular interrupted sutures technique at a median age of 10.2 years (range, 5.3 months–18.0 years). Median follow-up time was 5.2 years (range, 3 days–13.2 years). RESULTS: There were no deaths, but there were 3 reinterventions on the autograft for regurgitation and 2 resections of left ventricular outflow tract obstruction. There was no significant autograft stenosis, and freedom from moderate-to-severe regurgitation was 95% (95% confidence interval: 89–100) and 88% (95% confidence interval: 77–99) at 5 and 10 years, respectively. Median z-scores at the latest follow-up examination were, at the annulus, 0.31 [interquartile range (IQR) = −0.81 to 1.2]; at the sinus of Valsalva, 2.7 (IQR = 1.5–3.5); and at the sinotubular junction, 3.1 (IQR = 1.7–4.2). The correlation between z-scores and time after the operation was negative at the level of the annulus (r = −0.29, P = 0.034) but positive at the level of the sinus (r = +0.37, P = 0.005) and the sinotubular junction (r = +0.26, P = 0.068). The median rate of change in the z-score at the annulus was low, 0.065 z-score/year (IQR = −0.13 to 0.43). CONCLUSIONS: The subannular interrupted sutures implantation technique is associated with acceptable risks and, in the midterm, delivers limited annular dilatation, autograft regurgitation and delayed need for autograft reintervention

Quantitative cross-species extrapolation between humans and fish: The case of the anti-depressant fluoxetine

This article has been made available through the Brunel Open Access Publishing Fund.Fish are an important model for the pharmacological and toxicological characterization of human pharmaceuticals in drug discovery, drug safety assessment and environmental toxicology. However, do fish respond to pharmaceuticals as humans do? To address this question, we provide a novel quantitative cross-species extrapolation approach (qCSE) based on the hypothesis that similar plasma concentrations of pharmaceuticals cause comparable target-mediated effects in both humans and fish at similar level of biological organization (Read-Across Hypothesis). To validate this hypothesis, the behavioural effects of the anti-depressant drug fluoxetine on the fish model fathead minnow (Pimephales promelas) were used as test case. Fish were exposed for 28 days to a range of measured water concentrations of fluoxetine (0.1, 1.0, 8.0, 16, 32, 64 μg/L) to produce plasma concentrations below, equal and above the range of Human Therapeutic Plasma Concentrations (HTPCs). Fluoxetine and its metabolite, norfluoxetine, were quantified in the plasma of individual fish and linked to behavioural anxiety-related endpoints. The minimum drug plasma concentrations that elicited anxiolytic responses in fish were above the upper value of the HTPC range, whereas no effects were observed at plasma concentrations below the HTPCs. In vivo metabolism of fluoxetine in humans and fish was similar, and displayed bi-phasic concentration-dependent kinetics driven by the auto-inhibitory dynamics and saturation of the enzymes that convert fluoxetine into norfluoxetine. The sensitivity of fish to fluoxetine was not so dissimilar from that of patients affected by general anxiety disorders. These results represent the first direct evidence of measured internal dose response effect of a pharmaceutical in fish, hence validating the Read-Across hypothesis applied to fluoxetine. Overall, this study demonstrates that the qCSE approach, anchored to internal drug concentrations, is a powerful tool to guide the assessment of the sensitivity of fish to pharmaceuticals, and strengthens the translational power of the cross-species extrapolation

The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies

We review a sample of the early literature in which the reality of the expansion is discussed, explain Hubble's reticence to accept the expansion as real, and contrast the Tolman surface brightness test with three other modern tests. We search for the Tolman surface brightness depression with redshift using the Hubble Space Telescope (HST) data from Paper III for 34 early-type galaxies from the three clusters Cl 1324+3011 (z=0.76), Cl 1604+4304 (z=0.90), and Cl 1604+4321 (z=0.92). Depressions of the surface brightness relative to the zero-redshift fiducial lines in the mean surface brightness, log linear radius diagrams of Paper I are found for all three clusters. Expressed as the exponent, n, in 2.5 log (1 + z)^n mag, the value of n for all three clusters is n = 2.59 +/- 0.17 in the R band and 3.37 +/- 0.13 in the I band for a q_o = 1/2 model. The sensitivity of the result to the assumed value of q_o is shown to be less than 23% between q_o = 0 and +1. For a true Tolman signal with n = 4, the luminosity evolution in the look-back time, expressed as the exponent in 2.5 log (1+z)^(4-n) mag, must then be between 1.72 to 1.19 in the R band and 0.94 to 0.45 in the I band. We show that this is precisely the range expected from the evolutionary models of Bruzual & Charlot. We conclude that the Tolman surface brightness test is consistent with the reality of the expansion. We have also used the high-redshift HST data to test the ``tired light'' speculation for a non-expansion model for the redshift. The HST data rule out the ``tired light'' model at a significance level of better than 10 sigma.Comment: 36 pages, 6 figures; accepted for publication in the Astronomical Journa

Variants of ST8SIA1 Are Associated with Risk of Developing Multiple Sclerosis

Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system of unknown etiology with both genetic and environmental factors playing a role in susceptibility. To date, the HLA DR15/DQ6 haplotype within the major histocompatibility complex on chromosome 6p, is the strongest genetic risk factor associated with MS susceptibility. Additional alleles of IL7 and IL2 have been identified as risk factors for MS with small effect. Here we present two independent studies supporting an allelic association of MS with polymorphisms in the ST8SIA1 gene, located on chromosome 12p12 and encoding ST8 alpha-N-acetyl-neuraminide alpha-2,8-sialyltransferase 1. The initial association was made in a single three-generation family where a single-nucleotide polymorphism (SNP) rs4762896, was segregating together with HLA DR15/DQ6 in MS patients. A study of 274 family trios ( affected child and both unaffected parents) from Australia validated the association of ST8SIA1 in individuals with MS, showing transmission disequilibrium of the paternal alleles for three additional SNPs, namely rs704219, rs2041906, and rs1558793, with p = 0.001, p = 0.01 and p = 0.01 respectively. These findings implicate ST8SIA1 as a possible novel susceptibility gene for MS