Cohomology for infinitesimal unipotent algebraic and quantum groups

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its unipotent radical $U_J$, we determine the ring structure of the cohomology ring $H^\bullet((U_J)_1,k)$. We also obtain new results on computing $H^\bullet((P_J)_1,L(\lambda))$ as an $L_J$-module where $L(\lambda)$ is a simple $G$-module with high weight $\lambda$ in the closure of the bottom $p$-alcove. Finally, we provide generalizations of all our results to the quantum situation.Comment: 18 pages. Some proofs streamlined over previous version. Additional details added to some proofs in Section

Evaluation of cystatin C for the detection of chronic kidney disease in cats

BackgroundSerum cystatin C (sCysC) and urinary cystatin C (uCysC) are potential biomarkers for early detection of chronic kidney disease (CKD) in cats. An in-depth clinical validation is required. ObjectivesTo evaluate CysC as a marker for CKD in cats and to compare assay performance of the turbidimetric assay (PETIA) with the previously validated nephelometric assay (PENIA). AnimalsNinety cats were included: 49 CKD and 41 healthy cats. MethodsSerum CysC and uCysC concentrations were prospectively evaluated in cats with CKD and healthy cats. Based on plasma exo-iohexol clearance test (PexICT), sCysC was evaluated to distinguish normal, borderline, and low GFR. Sensitivity and specificity to detect PexICT<1.7mL/min/kg were calculated. Serum CysC results of PENIA and PETIA were correlated with GFR. Statistical analysis was performed using general linear modeling. ResultsCats with CKD had significantly higher meanSD sCysC (1.4 +/- 0.5mg/L) (P<.001) and uCysC/urinary creatinine (uCr) (291 +/- 411mg/mol) (P<.001) compared to healthy cats (sCysC 1.0 +/- 0.3 and uCysC/uCr 0.32 +/- 0.97). UCysC was detected in 35/49 CKD cats. R-2 values between GFR and sCysC or sCr were 0.39 and 0.71, respectively (sCysC or sCr=+GFR+epsilon). Sensitivity and specificity were 22 and 100% for sCysC and 83 and 93% for sCr. Serum CysC could not distinguish healthy from CKD cats, nor normal from borderline or low GFR, in contrast with sCr. ConclusionSerum CysC is not a reliable marker of reduced GFR in cats and uCysC could not be detected in all CKD cats

Accurate masses and radii of normal stars: modern results and applications

This paper presents and discusses a critical compilation of accurate, fundamental determinations of stellar masses and radii. We have identified 95 detached binary systems containing 190 stars (94 eclipsing systems, and alpha Centauri) that satisfy our criterion that the mass and radius of both stars be known to 3% or better. To these we add interstellar reddening, effective temperature, metal abundance, rotational velocity and apsidal motion determinations when available, and we compute a number of other physical parameters, notably luminosity and distance. We discuss the use of this information for testing models of stellar evolution. The amount and quality of the data also allow us to analyse the tidal evolution of the systems in considerable depth, testing prescriptions of rotational synchronisation and orbital circularisation in greater detail than possible before. The new data also enable us to derive empirical calibrations of M and R for single (post-) main-sequence stars above 0.6 M(Sun). Simple, polynomial functions of T(eff), log g and [Fe/H] yield M and R with errors of 6% and 3%, respectively. Excellent agreement is found with independent determinations for host stars of transiting extrasolar planets, and good agreement with determinations of M and R from stellar models as constrained by trigonometric parallaxes and spectroscopic values of T(eff) and [Fe/H]. Finally, we list a set of 23 interferometric binaries with masses known to better than 3%, but without fundamental radius determinations (except alpha Aur). We discuss the prospects for improving these and other stellar parameters in the near future.Comment: 56 pages including figures and tables. To appear in The Astronomy and Astrophysics Review. Ascii versions of the tables will appear in the online version of the articl

On small-noise equations with degenerate limiting system arising from volatility models

The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + \sigma X_{t}^{\gamma} dB_{t}, \ X_{0}=x, \ \gamma<1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of densities and implied volatilities in models involving instances of this equation, based on a careful implementation of saddle-point methods and (essentially) the explicit knowledge of Fourier transforms. Recent research on tail asymptotics for heat kernels [J-D. Deuschel, P.~Friz, A.~Jacquier, and S.~Violante. Marginal density expansions for diffusions and stochastic volatility, part II: Applications. 2013, arxiv:1305.6765] suggests to work with the rescaled variable $X^{\varepsilon}:=\varepsilon^{1/(1-\gamma)} X$: while allowing to turn a space asymptotic problem into a small-$\varepsilon$ problem with fixed terminal point, the process $X^{\varepsilon}$ satisfies a SDE in Wentzell--Freidlin form (i.e. with driving noise $\varepsilon dB$). We prove a pathwise large deviation principle for the process $X^{\varepsilon}$ as $\varepsilon \to 0$. As it will become clear, the limiting ODE governing the large deviations admits infinitely many solutions, a non-standard situation in the Wentzell--Freidlin theory. As for applications, the $\varepsilon$-scaling allows to derive exact log-asymptotics for path functionals of the process: while on the one hand the resulting formulae are confirmed by the CIR-CEV benchmarks, on the other hand the large deviation approach (i) applies to equations with a more general drift term and (ii) potentially opens the way to heat kernel analysis for higher-dimensional diffusions involving such an SDE as a component.Comment: 21 pages, 1 figur

Finite Schur filtration dimension for modules over an algebra with Schur filtration

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.Comment: 22 pages; final versio

Survey of the needs of patients with spinal cord injury: impact and priority for improvement in hand function in tetraplegics\ud

Objective: To investigate the impact of upper extremity deficit in subjects with tetraplegia.\ud \ud Setting: The United Kingdom and The Netherlands.\ud \ud Study design: Survey among the members of the Dutch and UK Spinal Cord Injury (SCI) Associations.\ud \ud Main outcome parameter: Indication of expected improvement in quality of life (QOL) on a 5-point scale in relation to improvement in hand function and seven other SCI-related impairments.\ud \ud Results: In all, 565 subjects with tetraplegia returned the questionnaire (overall response of 42%). Results in the Dutch and the UK group were comparable. A total of 77% of the tetraplegics expected an important or very important improvement in QOL if their hand function improved. This is comparable to their expectations with regard to improvement in bladder and bowel function. All other items were scored lower.\ud \ud Conclusion: This is the first study in which the impact of upper extremity impairment has been assessed in a large sample of tetraplegic subjects and compared to other SCI-related impairments that have a major impact on the life of subjects with SCI. The present study indicates a high impact as well as a high priority for improvement in hand function in tetraplegics.\ud \u

Persistence of the immune response induced by BCG vaccination.

BACKGROUND: Although BCG vaccination is recommended in most countries of the world, little is known of the persistence of BCG-induced immune responses. As novel TB vaccines may be given to boost the immunity induced by neonatal BCG vaccination, evidence concerning the persistence of the BCG vaccine-induced response would help inform decisions about when such boosting would be most effective. METHODS: A randomised control study of UK adolescents was carried out to investigate persistence of BCG immune responses. Adolescents were tested for interferon-gamma (IFN-gamma) response to Mycobacterium tuberculosis purified protein derivative (M.tb PPD) in a whole blood assay before, 3 months, 12 months (n = 148) and 3 years (n = 19) after receiving teenage BCG vaccination or 14 years after receiving infant BCG vaccination (n = 16). RESULTS: A gradual reduction in magnitude of response was evident from 3 months to 1 year and from 1 year to 3 years following teenage vaccination, but responses 3 years after vaccination were still on average 6 times higher than before vaccination among vaccinees. Some individuals (11/86; 13%) failed to make a detectable antigen-specific response three months after vaccination, or lost the response after 1 (11/86; 13%) or 3 (3/19; 16%) years. IFN-gamma response to Ag85 was measured in a subgroup of adolescents and appeared to be better maintained with no decline from 3 to 12 months. A smaller group of adolescents were tested 14 years after receiving infant BCG vaccination and 13/16 (81%) made a detectable IFN-gamma response to M.tb PPD 14 years after infant vaccination as compared to 6/16 (38%) matched unvaccinated controls (p = 0.012); teenagers vaccinated in infancy were 19 times more likely to make an IFN-gamma response of > 500 pg/ml than unvaccinated teenagers. CONCLUSION: BCG vaccination in infancy and adolescence induces immunological memory to mycobacterial antigens that is still present and measurable for at least 14 years in the majority of vaccinees, although the magnitude of the peripheral blood response wanes from 3 months to 12 months and from 12 months to 3 years post vaccination. The data presented here suggest that because of such waning in the response there may be scope for boosting anti-tuberculous immunity in BCG vaccinated children anytime from 3 months post-vaccination. This supports the prime boost strategies being employed for some new TB vaccines currently under development

Heavy Flavour Production at Tevatron and Parton Shower Effects

We present hadron-level predictions from the Monte Carlo generator Cascade and numerical calculations of charm and beauty production at the Fermilab Tevatron within the framework of the $k_T$-factorization QCD approach. Our consideration is based on the CCFM-evolved unintegrated gluon densities in a proton. The performed analysis covers the total and differential cross sections of open charm and beauty quarks, $B$ and $D$ mesons (or rather muons from their semileptonic decays) and the total and differential cross sections of $b \bar b$ di-jet hadroproduction. We study the theoretical uncertainties of our calculations and investigate the effects coming from parton showers in initial and final states. Our predictions are compared with the recent experimental data taken by the D0 and CDF collaborations. Special attention is put on the specific angular correlations between the final-state particles. We demonstrate that the final state parton shower plays a crucial role in the description of such observables. The decorrelated part of angular separations can be fully described, if the process $gg^*\rightarrow gg$ is included.Comment: Fig 8,9 10 replaced, small corrections in text A discussion of the delta phi results is adde

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

Winter wheat roots grow twice as deep as spring wheat roots, is this important for N uptake and N leaching losses?

Cropping systems comprising winter catch crops followed by spring wheat could reduce N leaching risks compared to traditional winter wheat systems in humid climates. We studied the soil mineral N (Ninorg) and root growth of winter- and spring wheat to 2.5 m depth during three years. Root depth of winter wheat (2.2 m) was twice that of spring wheat, and this was related to much lower amounts of Ninorg in the 1 to 2.5 m layer after winter wheat (81 kg Ninorg ha-1 less). When growing winter catch crops before spring wheat, N content in the 1 to 2.5 m layer after spring wheat was not different from that after winter wheat. The results suggest that by virtue of its deep rooting, winter wheat may not lead to high levels of leaching as it is often assumed in humid climates. Deep soil and root measurements (below 1 m) in this experiment were essential to answer the questions we posed