Diffusion-weighted MR imaging including bi-exponential fitting for the detection of recurrent or residual tumour after (chemo)radiotherapy for laryngeal and hypopharyngeal cancers

To assess whether diffusion-weighted magnetic resonance imaging (DW-MRI) including bi-exponential fitting helps to detect residual/recurrent tumours after (chemo)radiotherapy of laryngeal and hypopharyngeal carcinoma.

Bivariate meta-analysis of predictive values of diagnostic tests can be an alternative to bivariate meta-analysis of sensitivity and specificity

Meta-analysis of predictive values is usually discouraged because these values are directly affected by disease prevalence, but sensitivity and specificity sometimes show substantial heterogeneity as well. We propose a bivariate random-effects logitnormal model for the meta-analysis of the positive predictive value (PPV) and negative predictive value (NPV) of diagnostic tests.

T2 mapping in the knee after microfracture at 3.0 T: correlation of global T2 values and clinical outcome - preliminary results

OBJECTIVE: The aim of our study was to correlate global T2 values of microfracture repair tissue (RT) with clinical outcome in the knee joint. METHODS: We assessed 24 patients treated with microfracture in the knee joint. Magnetic resonance (MR) examinations were performed on a 3T MR unit, T2 relaxation times were obtained with a multi-echo spin-echo technique. T2 maps were obtained using a pixel wise, mono-exponential non-negative least squares fit analysis. Slices covering the cartilage RT were selected and region of interest analysis was done. An individual T2 index was calculated with global mean T2 of the RT and global mean T2 of normal, hyaline cartilage. The Lysholm score and the International Knee Documentation Committee (IKDC) knee evaluation forms were used for the assessment of clinical outcome. Bivariate correlation analysis and a paired, two tailed t test were used for statistics. RESULTS: Global T2 values of the RT [mean 49.8ms, standards deviation (SD) 7.5] differed significantly (P<0.001) from global T2 values of normal, hyaline cartilage (mean 58.5ms, SD 7.0). The T2 index ranged from 61.3 to 101.5. We found the T2 index to correlate with outcome of the Lysholm score (r(s)=0.641, P<0.001) and the IKDC subjective knee evaluation form (r(s)=0.549, P=0.005), whereas there was no correlation with the IKDC knee form (r(s)=-0.284, P=0.179). CONCLUSION: These findings indicate that T2 mapping is sensitive to assess RT function and provides additional information to morphologic MRI in the monitoring of microfracture.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Quasi-Self-Dual Exponential Lévy Processes

The important application of semistatic hedging in financial markets naturally leads to the notion of quasi--self-dual processes. The focus of our study is to give new characterizations of quasi--self-duality. We analyze quasi--self-dual Lévy driven markets which do not admit arbitrage opportunities and derive a set of equivalent conditions for the stochastic logarithm of quasi--self-dual martingale models. Since for nonvanishing order parameter two martingale properties have to be satisfied simultaneously, there is a nontrivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known Lévy-driven models, we derive a family of closed-form inversion formulae.