Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Bone Volume Fraction and Fabric Anisotropy Are Better Determinants of Trabecular Bone Stiffness than Other Morphological Variables

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphologyelasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae and iliac crest were analysed. Their morphology was assessed via 25 variables and their stiffness tensor (inline image) was computed from six independent load cases using micro finite element analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multi-linear regression modelling the dependent variable inline image. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of inline image (inline image=0.889), especially in combination with fabric (inline image=0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (inline image=0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and post-elastic properties.

Von Willebrand Factor Improves Risk Prediction in Addition to N-Terminal Pro-B-type Natriuretic Peptide in Patients Referred to Coronary Angiography and Signs and Symptoms of Heart Failure and Preserved Ejection Fraction.

BACKGROUND Heart failure with preserved ejection fraction (HFpEF) represents a growing health burden associated with substantial mortality and morbidity. Consequently, risk prediction is of highest importance. Endothelial dysfunction has been recently shown to play an important role in the complex pathophysiology of HFpEF. We therefore aimed to assess von Willebrand factor (vWF), a marker of endothelial damage, as potential biomarker for risk assessment in patients with HFpEF. METHODS AND RESULTS Concentrations of vWF were assessed in 457 patients with HFpEF enrolled as part of the LUdwigshafen Risk and Cardiovascular Health (LURIC) study. All-cause mortality was observed in 40% of patients during a median follow-up time of 9.7 years. vWF significantly predicted mortality with a hazard ratio (HR) per increase of 1 SD of 1.45 (95% confidence interval, 1.26-1.68; P<0.001) and remained a significant predictor after adjustment for age, sex, body mass index, N-terminal pro-B-type natriuretic peptide (NT-proBNP), renal function, and frequent HFpEF-related comorbidities (adjusted HR per 1 SD, 1.22; 95% confidence interval, 1.05-1.42; P=0.001). Most notably, vWF showed additional prognostic value beyond that achievable with NT-proBNP indicated by improvements in C-Statistic (vWF×NT-proBNP: 0.65 versus NT-proBNP: 0.63; P for comparison, 0.004) and category-free net reclassification index (37.6%; P<0.001). CONCLUSIONS vWF is an independent predictor of long-term outcome in patients with HFpEF, which is in line with endothelial dysfunction as potential mediator in the pathophysiology of HFpEF. In particular, combined assessment of vWF and NT-proBNP improved risk prediction in this vulnerable group of patients.

Impact of mitral regurgitation on clinical outcomes of patients with low-ejection fraction, low-gradient severe aortic stenosis undergoing transcatheter aortic valve implantation.

BACKGROUND Up to 1 in 6 patients undergoing transcatheter aortic valve implantation (TAVI) present with low-ejection fraction, low-gradient (LEF-LG) severe aortic stenosis and concomitant relevant mitral regurgitation (MR) is present in 30% to 55% of these patients. The effect of MR on clinical outcomes of LEF-LG patients undergoing TAVI is unknown. METHODS AND RESULTS Of 606 consecutive patients undergoing TAVI, 113 (18.7%) patients with LEF-LG severe aortic stenosis (mean gradient ≤40 mm Hg, aortic valve area <1.0 cm(2), left ventricular ejection fraction <50%) were analyzed. LEF-LG patients were dichotomized into ≤mild MR (n=52) and ≥moderate MR (n=61). Primary end point was all-cause mortality at 1 year. No differences in mortality were observed at 30 days (P=0.76). At 1 year, LEF-LG patients with ≥moderate MR had an adjusted 3-fold higher rate of all-cause mortality (11.5% versus 38.1%; adjusted hazard ratio, 3.27 [95% confidence interval, 1.31-8.15]; P=0.011), as compared with LEF-LG patients with ≤mild MR. Mortality was mainly driven by cardiac death (adjusted hazard ratio, 4.62; P=0.005). As compared with LEF-LG patients with ≥moderate MR assigned to medical therapy, LEF-LG patients with ≥moderate MR undergoing TAVI had significantly lower all-cause mortality (hazard ratio, 0.38; 95% confidence interval, 0.019-0.75) at 1 year. CONCLUSIONS Moderate or severe MR is a strong independent predictor of late mortality in LEF-LG patients undergoing TAVI. However, LEF-LG patients assigned to medical therapy have a dismal prognosis independent of MR severity suggesting that TAVI should not be withheld from symptomatic patients with LEF-LG severe aortic stenosis even in the presence of moderate or severe MR.

Microscopic theory of cooperative spin crossover: Interaction of molecular modes with phonons

In this article, we present a new microscopic theoretical approach to the description of spin crossover in molecular crystals. The spin crossover crystals under consideration are composed of molecular fragments formed by the spin-crossover metal ion and its nearest ligand surrounding and exhibiting well defined localized (molecular) vibrations. As distinguished from the previous models of this phenomenon, the developed approach takes into account the interaction of spin-crossover ions not only with the phonons but also a strong coupling of the electronic shells with molecular modes. This leads to an effective coupling of the local modes with phonons which is shown to be responsible for the cooperative spin transition accompanied by the structural reorganization. The transition is characterized by the two order parameters representing the mean values of the products of electronic diagonal matrices and the coordinates of the local modes for the high- and low-spin states of the spin crossover complex. Finally, we demonstrate that the approach provides a reasonable explanation of the observed spin transition in the [Fe(ptz)6](BF4)2 crystal. The theory well reproduces the observed abrupt low-spin → high-spin transition and the temperature dependence of the high-spin fraction in a wide temperature range as well as the pronounced hysteresis loop. At the same time within the limiting approximations adopted in the developed model, the evaluated high-spin fraction vs. T shows that the cooperative spin-lattice transition proves to be incomplete in the sense that the high-spin fraction does not reach its maximum value at high temperature.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Seasonal variation of high-molecular-weight compounds in the water-soluble fraction of organic urban aerosols

Aerosol samples were collected in Zurich, Switzerland, at an urban background site and were analyzed with size exclusion chromatography (SEC) and laser/desorption ionization mass spectrometry (LDI-MS) for water-soluble organic compounds with high molecular weight. Daily samples were collected during two campaigns in winter and summer, for 1 month each. The concentration of high-molecular-weight compounds (humic-like substances (HULIS)) was between 0.4 and 4 μg/m3 in winter and summer. The most intense signals in the LDI-MS mass spectra were measured between m/z150 and 500, comparing well with the mode of the two main high mass peaks determined with SEC corresponding to masses between 200 and 600 Da. For the maximum molecular weight, however, different results were obtained by the two techniques: whereas a maximum molecular weight between 1300 and 3300 Da was found with SEC, hardly any peaks above m/z700 were measured with LDI-MS. During summer the maximum molecular weight of HULIS (determined with SEC) correlates positively with several parameters such as ozone and increased temperature indicative of enhanced atmospheric photo-oxidation. The HULIS concentration also correlates positively with the oxalic acid concentration in the particles. This suggests that HULIS are generated by secondary processes in summer. The lack of such correlations during winter suggests that other sources and processes might be important during colder seasons.

Das Ministerium Brandenburg und die Fraction Unruh, und Eiserner Bestand an Regierungs-Rechten, ohne welche ein Staat überhaupt nicht lebensfähig ist

Boberach: Weil Völker nicht selten an ihren politischen Ideen zugrundegehen, war auch Preußen durch die Politik der Linken bedroht und das Ministerium hat die dem Staat gebührenden Regierungsfunktionen mit Recht in Anspruch genommen

Hepatocellular Carcinoma Screening With Computed Tomography Using the Arterial Enhancement Fraction With Radiologic-Pathologic Correlation.

OBJECTIVE The aim of this study was to investigate the performance of the arterial enhancement fraction (AEF) in multiphasic computed tomography (CT) acquisitions to detect hepatocellular carcinoma (HCC) in liver transplant recipients in correlation with the pathologic analysis of the corresponding liver explants. MATERIALS AND METHODS Fifty-five transplant recipients were analyzed: 35 patients with 108 histologically proven HCC lesions and 20 patients with end-stage liver disease without HCC. Six radiologists looked at the triphasic CT acquisitions with the AEF maps in a first readout. For the second readout without the AEF maps, 3 radiologists analyzed triphasic CT acquisitions (group 1), whereas the other 3 readers had 4 contrast acquisitions available (group 2). A jackknife free-response reader receiver operating characteristic analysis was used to compare the readout performance of the readers. Receiver operating characteristic analysis was used to determine the optimal cutoff value of the AEF. RESULTS The figure of merit (θ = 0.6935) for the conventional triphasic readout was significantly inferior compared with the triphasic readout with additional use of the AEF (θ = 0.7478, P < 0.0001) in group 1. There was no significant difference between the fourphasic conventional readout (θ = 0.7569) and the triphasic readout (θ = 0.7615, P = 0.7541) with the AEF in group 2. Without the AEF, HCC lesions were detected with a sensitivity of 30.7% (95% confidence interval [CI], 25.5%-36.4%) and a specificity of 97.1% (96.0%-98.0%) by group 1 looking at 3 CT acquisition phases and with a sensitivity of 42.1% (36.2%-48.1%) and a specificity of 97.5% (96.4%-98.3%) in group 2 looking at 4 CT acquisition phases. Using the AEF maps, both groups looking at the same 3 acquisition phases, the sensitivity was 47.7% (95% CI, 41.9%-53.5%) with a specificity of 97.4% (96.4%-98.3%) in group 1 and 49.8% (95% CI, 43.9%-55.8%)/97.6% (96.6%-98.4%) in group 2. The optimal cutoff for the AEF was 50%. CONCLUSION The AEF is a helpful tool to screen for HCC with CT. The use of the AEF maps may significantly improve HCC detection, which allows omitting the fourth CT acquisition phase and thus making a 25% reduction of radiation dose possible.

Saddlepoint approximations

The saddlepoint method provides accurate approximations for the distributions of many test statistics, estimators and for important probabilities arising in various stochastic models. The saddlepoint approximation is a large deviations technique which is substantially more accurate than limiting normal or Edgeworth approximations, especially in presence of very small sample sizes or very small probabilities. The outstanding accuracy of the saddlepoint approximation can be explained by the fact that it has bounded relative error.

Inhalation anesthesia of rats: influence of the fraction of inspired oxygen on limb ischemia/reperfusion injury

Inhalation anesthesia with isoflurane is a well-established and safe method used in small laboratory animals. In most cases oxygen is used as a carrier gas for isoflurane, but room air or mixtures of oxygen with air or nitrous oxide are also being used. Anesthesia is therefore administered using different fractions of inspired oxygen (FiO2), and this may have consequences for the outcome of experiments. The aim of the present study was to investigate the influence of FiO2 on rat hind limb ischemia/reperfusion injury and to refine the used inhalation anesthesia. Male Wistar rats were subjected to 3.5 h of ischemia and 2 h of reperfusion, and divided into three groups according to FiO2 in the O2/air/isoflurane anesthesia gas mixture: 40%, 60%, and 100% O2. Normal, healthy rats were used as controls. Muscle edema and creatine kinase MM, a marker for myocyte necrosis, were significantly increased with 40% FiO2 as compared with 100% FiO2 (P<0.05). Partial pressure of oxygen, oxygen saturation, and oxyhemoglobin were significantly higher in the 100% O2 group as compared with 40% O2. No significant differences were detected for other parameters, such as the oxidative stress markers malondialdehyde and superoxide dismutase. We conclude that a refined inhalation anesthesia setting using 40% FiO2, reflecting more or less the clinical situation, leads to a more severe and more physiologically relevant reperfusion injury than higher FiO2. Oxidative stress did not correlate with FiO2 and seemed to have no influence on reperfusion injury.

Fibroblast Growth Factor 23 Is an Independent and Specific Predictor of Mortality in Patients With Heart Failure and Reduced Ejection Fraction

BACKGROUND Strategies to improve risk prediction are of major importance in patients with heart failure (HF). Fibroblast growth factor 23 (FGF-23) is an endocrine regulator of phosphate and vitamin D homeostasis associated with an increased cardiovascular risk. We aimed to assess the prognostic effect of FGF-23 on mortality in HF patients with a particular focus on differences between patients with HF with preserved ejection fraction and patients with HF with reduced ejection fraction (HFrEF). METHODS AND RESULTS FGF-23 levels were measured in 980 patients with HF enrolled in the Ludwigshafen Risk and Cardiovascular Health (LURIC) study including 511 patients with HFrEF and 469 patients with HF with preserved ejection fraction and a median follow-up time of 8.6 years. FGF-23 was additionally measured in a second cohort comprising 320 patients with advanced HFrEF. FGF-23 was independently associated with mortality with an adjusted hazard ratio per 1-SD increase of 1.30 (95% confidence interval, 1.14-1.48; P<0.001) in patients with HFrEF, whereas no such association was found in patients with HF with preserved ejection fraction (for interaction, P=0.043). External validation confirmed the significant association with mortality with an adjusted hazard ratio per 1 SD of 1.23 (95% confidence interval, 1.02-1.60; P=0.027). FGF-23 demonstrated an increased discriminatory power for mortality in addition to N-terminal pro-B-type natriuretic peptide (C-statistic: 0.59 versus 0.63) and an improvement in net reclassification index (39.6%; P<0.001). CONCLUSIONS FGF-23 is independently associated with an increased risk of mortality in patients with HFrEF but not in those with HF with preserved ejection fraction, suggesting a different pathophysiologic role for both entities.

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.