A spectral method for elliptic equations: the Dirichlet problem

An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method is applied to the reformulated problem, using multivariate polynomials as the approximants. For a smooth boundary and smooth problem parameter functions, the method is proven to converge faster than any power of 1/n with n the degree of the approximate Galerkin solution. Examples in two and three variables are given as numerical illustrations. Empirically, the condition number of the associated linear system increases like O(N), with N the order of the linear system.Comment: This is latex with the standard article style, produced using Scientific Workplace in a portable format. The paper is 22 pages in length with 8 figure

Overexpression of aurora B kinase (AURKB) in primary non-small cell lung carcinoma is frequent, generally driven from one allele, and correlates with the level of genetic instability

Aurora kinases are key regulators of chromosome segregation during mitosis. We have previously shown by microarray analysis of primary lung carcinomas and matched normal tissue that AURKB (22 out of 37) and AURKA (15 out of 37) transcripts are frequently over-represented in these tumours. We now confirm these observations in a second series of 44 carcinomas and also show that aurora B kinase protein levels are raised in the tumours compared to normal tissue. Elevated levels of expression in tumours are not a consequence of high-level amplification of the AURKB gene. Using a coding sequence polymorphism we show that in most cases (seven out of nine) tumour expression is predominantly driven from one AURKB allele. Given the function of aurora B kinase, we examined whether there was an association between expression levels and genetic instability. We defined two groups of high and low AURKB expression. Using a panel of 10 microsatellite markers, we found that the group showing the higher level of expression had a higher frequency of allelic imbalance (P=0.0012). Analysis of a number of other genes that are strongly and specifically expressed in tumour over normal lung, including SERPINB5, TERT and PRAME, showed marked allelic expression imbalances in the tumour tissue in the context of balanced or only marginally imbalanced relative allelic copy numbers. Our data support a model of early carcinogenesis wherein defects in the process of inactivation of lung stem-cell associated genes during differentiation, contributes to the development of carcinogenesis

Numerical analysis of quasinormal modes in nearly extremal Schwarzschild-de Sitter spacetimes

We calculate high-order quasinormal modes with large imaginary frequencies for electromagnetic and gravitational perturbations in nearly extremal Schwarzschild-de Sitter spacetimes. Our results show that for low-order quasinormal modes, the analytical approximation formula in the extremal limit derived by Cardoso and Lemos is a quite good approximation for the quasinormal frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where $r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity, respectively. For high-order quasinormal modes, to which corresponds quasinormal frequencies with large imaginary parts, on the other hand, this formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find that the real parts of the quasinormal frequencies have oscillating behaviors in the limit of highly damped modes, which are similar to those observed in the case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating ${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where $\omega$ denotes the quasinormal frequency. This means that for gravitational perturbations, the real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter spacetime appears not to approach any constant value in the limit of highly damped modes. On the other hand, for electromagnetic perturbations, the real part of frequency seems to go to zero in the limit.Comment: 9 pages, 7 figures, to appear in Physical Review

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

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.Comment: 25 pages in latex, no figures, content changed, corrections to Newton's law included for smooth version of RS model and an author adde

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