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

Quasinormal modes and stability of the rotating acoustic black hole: numerical analysis

The study of the quasinormal modes (QNMs) of the 2+1 dimensional rotating draining bathtub acoustic black hole, the closest analogue found so far to the Kerr black hole, is performed. Both the real and imaginary parts of the quasinormal (QN) frequencies as a function of the rotation parameter B are found through a full non-linear numerical analysis. Since there is no change in sign in the imaginary part of the frequency as B is increased we conclude that the 2+1 dimensional rotating draining bathtub acoustic black hole is stable against small perturbations.Comment: 6 pages, ReVTeX4. v2. References adde

Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure

Stability of Impurities with Coulomb Potential in Graphene with Homogeneous Magnetic Field

Given a 2-dimensional no-pair Weyl operator with a point nucleus of charge Z, we show that a homogeneous magnetic field does not lower the critical charge beyond which it collapses.Comment: J. Math. Phys. (in press

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

The scalar perturbation of the higher-dimensional rotating black holes

The massless scalar field in the higher-dimensional Kerr black hole (Myers- Perry solution with a single rotation axis) has been investigated. It has been shown that the field equation is separable in arbitrary dimensions. The quasi-normal modes of the scalar field have been searched in five dimensions using the continued fraction method. The numerical result shows the evidence for the stability of the scalar perturbation of the five-dimensional Kerr black holes. The time scale of the resonant oscillation in the rapidly rotating black hole, in which case the horizon radius becomes small, is characterized by (black hole mass)^{1/2}(Planck mass)^{-3/2} rather than the light-crossing time of the horizon.Comment: 16 pages, 7 figures, revised versio

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population Histories

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure -- the history of multiple subpopulations that merge, split and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.Comment: 38 pages, Appeared in RECOMB 201

Neoadjuvant chemoradiotherapy with or without panitumumab in patients with wild-type KRAS, locally advanced rectal cancer (LARC): a randomized, multicenter, phase II trial SAKK 41/07

Background We conducted a randomized, phase II, multicenter study to evaluate the anti-epidermal growth factor receptor (EGFR) mAb panitumumab (P) in combination with chemoradiotherapy (CRT) with standard-dose capecitabine as neoadjuvant treatment for wild-type KRAS locally advanced rectal cancer (LARC). Patients and methods Patients with wild-type KRAS, T3-4 and/or N+ LARC were randomly assigned to receive CRT with or without P (6 mg/kg). The primary end-point was pathological near-complete or complete tumor response (pNC/CR), defined as grade 3 (pNCR) or 4 (pCR) histological regression by Dworak classification (DC). Results Forty of 68 patients were randomly assigned to P + CRT and 28 to CRT. pNC/CR was achieved in 21 patients (53%) treated with P + CRT [95% confidence interval (CI) 36%-69%] versus 9 patients (32%) treated with CRT alone (95% CI: 16%-52%). pCR was achieved in 4 (10%) and 5 (18%) patients, and pNCR in 17 (43%) and 4 (14%) patients. In immunohistochemical analysis, most DC 3 cells were not apoptotic. The most common grade ≥3 toxic effects in the P + CRT/CRT arm were diarrhea (10%/6%) and anastomotic leakage (15%/4%). Conclusions The addition of panitumumab to neoadjuvant CRT in patients with KRAS wild-type LARC resulted in a high pNC/CR rate, mostly grade 3 DC. The results of both treatment arms exceeded prespecified thresholds. The addition of panitumumab increased toxicit