Asymptotic and exact series representations for the incomplete Gamma function

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of $\Gamma(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.Comment: 8 pages, 4 figure

Thyroid hormones, blood plasma metabolites and haematological parameters in relationship to milk yield in dairy cows

To study their relationship to milk yield, the concentrations, in jugular venous blood, of thyroxine iodine (T4I), thyroxine (T4), 3,5,3'-tri-iodothyronine (T3), glucose, non-esterified fatty acids (NEFA), triglycerides, phospholipids, cholesterol, total protein, albumin, urea, haemoglobin and packed cell volume (PCV) have been measured in 36 cows (Simmental, Swiss Brown, Holstein and Simmental × Holstein) of different ages during a full lactation, pregnancy, dry period, parturition and 150 days of the ensuing lactation. Thyroid hormones and triglycerides were negatively, and total protein, globulin, cholesterol and phospholipids were positively, correlated with uncorrected or corrected milk yield during several periods of lactation, whereas glucose, NEFA, albumin, urea, haemoglobin and packed cell volume were not correlated with milk yield. The 10 animals with the highest milk yield (18·9 to 23·5 kg/day) exhibited significantly lower values of T4I, T4, T3 and glucose, significantly higher levels of total protein and globulin and tended to have higher levels of NEFA than the 10 cows with the lowest milk yield (10·9 to 14·3 kg/day) throughout or during certain periods of lactation, whereas concentrations of triglycerides, phospholipids, cholesterol, albumin, haemoglobin and PCV did not differ. Changes in T4I, T4, T3, glucose and total protein during lactation were also influenced by age, presumably associated with an increase in milk production with age. T3 was consistently lowest and cholesterol and phospholipids, during later stages of lactation, were highest in Holsteins, which had the highest milk yields of all breeds. Changes of blood parameters were mainly caused by shifts in energy and protein metabolism in association with level of milk productio

Superradiant instabilities of rotating black branes and strings

Black branes and strings are generally unstable against a certain sector of gravitational perturbations. This is known as the Gregory-Laflamme instability. It has been recently argued that there exists another general instability affecting many rotating extended black objects. This instability is in a sense universal, in that it is triggered by any massless field, and not just gravitational perturbations. Here we investigate this novel mechanism in detail. For this instability to work, two ingredients are necessary: (i) an ergo-region, which gives rise to superradiant amplification of waves, and (ii) ``bound'' states in the effective potential governing the evolution of the particular mode under study. We show that the black brane Kerr_4 x R^p is unstable against this mechanism, and we present numerical results for instability timescales for this case. On the other hand, and quite surprisingly, black branes of the form Kerr_d x R^p are all stable against this mechanism for d>4. This is quite an unexpected result, and it stems from the fact that there are no stable circular orbits in higher dimensional black hole spacetimes, or in a wave picture, that there are no bound states in the effective potential. We also show that it is quite easy to simulate this instability in the laboratory with acoustic black branes.Comment: 19 pages, 10 figures. v2: Enlarged discussion on the necessary conditions for the existence of instabilit

Efficacy and safety of secukinumab for the treatment of severe ABCA12 deficiency‐related ichthyosis in a child

Summary Background Patients with severe autosomal recessive congenital ichthyosis (ARCI) show a T helper 17/interleukin 17 (Th17/IL17) skewing in their skin and serum, resembling the inflammatory profile of psoriatic patients. Secukinumab, an IL‐17A inhibitor, has shown clinical efficacy in patients with moderate‐to‐severe plaque psoriasis. Aims To test the clinical efficacy and safety of secukinumab in a paediatric patient with ATP‐binding cassette subfamily A member 12 deficiency‐related severe erythrodermic ARCI. Materials & Methods 6‐months therapeutic trial. During the first 4‐weeks induction period, the patient received weekly subcutaneous injections of 150 mg secukinumab (five injections in total). During the following 20‐weeks maintenance period, the patient was given a subcutaneous injection of 150 mg secukinumab every 4 weeks. Result & Discussion After the 6‐months therapy period, there was a 48% reduction from the baseline Ichthyosis‐Area‐Severity‐Index (‐Erythema/‐Scaling) score. The treatment was well tolerated. Moreover, cytokine analysis revealed a reduction of keratinocyte‐derived proinflammatory cytokines and an abrogation of Th17‐skewing during therapy. Conclusion Further studies are needed to evaluate the effects of the use of IL‐17A inhibition in ARCI patients

On the Spectrum of Field Quadratures for a Finite Number of Photons

The spectrum and eigenstates of any field quadrature operator restricted to a finite number $N$ of photons are studied, in terms of the Hermite polynomials. By (naturally) defining \textit{approximate} eigenstates, which represent highly localized wavefunctions with up to $N$ photons, one can arrive at an appropriate notion of limit for the spectrum of the quadrature as $N$ goes to infinity, in the sense that the limit coincides with the spectrum of the infinite-dimensional quadrature operator. In particular, this notion allows the spectra of truncated phase operators to tend to the complete unit circle, as one would expect. A regular structure for the zeros of the Christoffel-Darboux kernel is also shown.Comment: 16 pages, 11 figure

Generalized Fermi-Dirac Functions and Derivatives: Properties and Evaluation

The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac functions have been found. An effective numerical method to evaluate the derivatives of the generalized Fermi-Dirac functions up to third order with respect to both degeneracy and temperature is then proposed, following Aparicio. A Fortran program based on this method, together with a sample test case, is provided. Accuracy and domain of reliability of some other, popularly used analytic approximations of the generalized Fermi-Dirac functions for extreme conditions are investigated and compared with our results.Comment: accepted for publication in Comp. Phys. Com

Convergence rate for numerical computation of the lattice Green's function

Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the singular subspace, corresponding to uniform displacements and forces for the infinite lattice. Three different techniques--relative displacement, elastic Green's function, and discontinuity correction--have different computational complexity for a specified numerical error. We calculate the convergence rates for elastically isotropic and anisotropic cases and compare them to analytic results. Our results confirm that the discontinuity correction is the most computationally efficient method to compute the lattice Green's function.Comment: 12 pages, 4 figure

Influence of mycophenolate mofetil dosage and plasma levels on the occurrence of chronic lung allograft dysfunction in lung transplants: a retrospective cohort analysis

INTRODUCTION: Development of chronic lung allograft dysfunction is a limiting factor for post-lung transplant survival. We evaluated whether the dose of the immunosuppressant mycophenolate mofetil or plasma concentrations of the active metabolite mycophenolic acid affect the development of chronic lung allograft dysfunction. METHODS: In this retrospective cohort study we recruited 71 patients with a lung transplant between 2010 and 2014 which survived the first year after transplantation up to 1 July 2021. An event-time-analytical Cox proportional-hazards regression model with time-varying-covariates (18,431 measurements for MPA, mycophenolate mofetil dosage, lymphocytes) was used to predict chronic lung allograft dysfunction, with adjustment for sociodemographic factors and lung function at baseline. RESULTS: 37 patients did not develop chronic lung allograft dysfunction (age 41.3 ± 15.6 years, baseline FEV1 95.5 ± 19.1% predicted) and 34 patients developed chronic lung allograft dysfunction (age 50.9 ± 13.3 years, baseline FEV1 102.2 ± 25.4% predicted). Mean mycophenolic acid did not differ significantly between the groups (2.8 ± 1.7 and 3.0 ± 2.3 mg/l; p = 0.724). In the first 4 post-transplant years the death rate was 25%. A total of 50% of the patients died by the ninth post-transplant year. There was a dose-effect relationship between mycophenolate mofetil dosage, mycophenolic acid (r2 = 0.02, p <0.001), as well as lymphocyte levels (r2 = –0.007, p <0.001), but only the traditional risk factor age predicted chronic lung allograft dysfunction. Continuously measured mycophenolic acid did not predict chronic lung allograft dysfunction (hazard ratio 0.98, 95% confidence interval 0.90–1.06, p = 0.64 over a period of 382.97 patient-years). CONCLUSION: Mycophenolate mofetil dosage and mycophenolic acid were not associated with chronic lung allograft dysfunction development. Thus, the mycophenolate mofetil dose or mycophenolic acid plasma concentration are not a primary factor related to organ rejection, but chronic lung allograft dysfunction may be influenced by other components of immunosuppression or other factors

Scalar perturbations of higher dimensional rotating and ultra-spinning black holes

We investigate the stability of higher dimensional rotating black holes against scalar perturbations. In particular, we make a thorough numerical and analytical analysis of six-dimensional black holes, not only in the low rotation regime but in the high rotation regime as well. Our results suggest that higher dimensional Kerr black holes are stable against scalar perturbations, even in the ultra-spinning regime.Comment: 7 pages, ReVTeX