Bounds on the density of sources of ultra-high energy cosmic rays from the Pierre Auger Observatory

We derive lower bounds on the density of sources of ultra-high energy cosmic rays from the lack of significant clustering in the arrival directions of the highest energy events detected at the Pierre Auger Observatory. The density of uniformly distributed sources of equal intrinsic intensity was found to be larger than ~(0.06 - 5) × '10 POT. -4' 'Mpc POT. -3' at 95% CL, depending on the magnitude of the magnetic deflections. Similar bounds, in the range (0.2 - 7) × '10 POT. -4' 'Mpc POT. -3', were obtained for sources following the local matter distribution.

High precision swept volume approximation with conservative error bounds

In technical design processes in the automotive industry, digital prototypes rapidly gain importance, because they allow for a detection of design errors in early development stages. The technical design process includes the computation of swept volumes for maintainability analysis and clearance checks. The swept volume is very useful, for example, to identify problem areas where a safety distance might not be kept. With the explicit construction of the swept volume an engineer gets evidence on how the shape of components that come too close have to be modified.rnIn this thesis a concept for the approximation of the outer boundary of a swept volume is developed. For safety reasons, it is essential that the approximation is conservative, i.e., that the swept volume is completely enclosed by the approximation. On the other hand, one wishes to approximate the swept volume as precisely as possible. In this work, we will show, that the one-sided Hausdorff distance is the adequate measure for the error of the approximation, when the intended usage is clearance checks, continuous collision detection and maintainability analysis in CAD. We present two implementations that apply the concept and generate a manifold triangle mesh that approximates the outer boundary of a swept volume. Both algorithms are two-phased: a sweeping phase which generates a conservative voxelization of the swept volume, and the actual mesh generation which is based on restricted Delaunay refinement. This approach ensures a high precision of the approximation while respecting conservativeness.rnThe benchmarks for our test are amongst others real world scenarios that come from the automotive industry.rnFurther, we introduce a method to relate parts of an already computed swept volume boundary to those triangles of the generator, that come closest during the sweep. We use this to verify as well as to colorize meshes resulting from our implementations.

Non-water-suppressed proton MR spectroscopy improves spectral quality in the human spinal cord

Magnetic resonance spectroscopy enables insight into the chemical composition of spinal cord tissue. However, spinal cord magnetic resonance spectroscopy has rarely been applied in clinical work due to technical challenges, including strong susceptibility changes in the region and the small cord diameter, which distort the lineshape and limit the attainable signal to noise ratio. Hence, extensive signal averaging is required, which increases the likelihood of static magnetic field changes caused by subject motion (respiration, swallowing), cord motion, and scanner-induced frequency drift. To avoid incoherent signal averaging, it would be ideal to perform frequency alignment of individual free induction decays before averaging. Unfortunately, this is not possible due to the low signal to noise ratio of the metabolite peaks. In this article, frequency alignment of individual free induction decays is demonstrated to improve spectral quality by using the high signal to noise ratio water peak from non-water-suppressed proton magnetic resonance spectroscopy via the metabolite cycling technique. Electrocardiography (ECG)-triggered point resolved spectroscopy (PRESS) localization was used for data acquisition with metabolite cycling or water suppression for comparison. A significant improvement in the signal to noise ratio and decrease of the Cramér Rao lower bounds of all metabolites is attained by using metabolite cycling together with frequency alignment, as compared to water-suppressed spectra, in 13 healthy volunteers.

Lower complexity bounds in justification logic

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in~NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound. The proof method is then extended to provide a uniform proof that the corresponding full pure justification logics are $\Pi^p_2$-hard, reproving and generalizing an earlier result by Milnikel.

Semiparametric Theory for Causal Mediation Analysis: efficiency bounds, multiple robustness, and sensitivity analysis

Whilst estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of the exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Although powerful semiparametric methodologies have been developed to analyze observational studies, that produce double robust and highly efficient estimates of the marginal total causal effect, similar methods for mediation analysis are currently lacking. Thus, this paper develops a general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables. Our analytic framework is particularly appealing, because it gives new insights on issues of efficiency and robustness in the context of mediation analysis. In particular, we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects, and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable.

IgE-bearing cells in bronchoalveolar lavage fluid and allergen-specific IgE levels in sera from RAO-affected horses

Recurrent airway obstruction (RAO) is a common condition in stabled horses characterized by small airway inflammation, airway neutrophilia and obstruction following exposure of susceptible horses to mouldy hay and straw and is thus regarded as a hypersensitivity reaction to mould spores. However, the role of immunoglobulin E antibodies (IgE) in the pathogenesis of RAO is unclear. We hypothesized that the number of cells with receptor-bound IgE in bronchoalveolar lavage fluid (BALF) and IgE levels in serum would be higher in RAO-affected than in healthy horses living in the same environment. Therefore, IgE-positive (+) cells were identified by immunocytochemistry on cytospins from BALF and counted. IgE levels against the mould extracts Aspergillus fumigatus (Asp. f.) and Alternaria alternata (Alt. a.) and the recombinant mould allergen Aspergillus fumigatus 8 (rAsp f 8) were measured by enzyme-linked immunosorbent assay (ELISA) in the sera of seven RAO-affected and 22 clinically healthy mature horses housed in the same conventional stable environment. After correcting for the number of neutrophils, there were no significant differences in IgE+ cells on cytospins from BALF between both groups of horses (5% versus 7%, P > 0.1). Serum IgE levels against the mould extracts were significantly higher in RAO-affected than in clinically healthy horses [median = 119 versus 66 relative ELISA units (REU), P < 0.05]. Furthermore, significantly more RAO-affected than healthy horses had detectable serum IgE against the recombinant allergen rAsp f 8 (4/7 and 3/22, respectively, P < 0.05). Age had no significant effect on BALF cell ratios or on specific serum IgE levels. These results show that high IgE levels against mould antigens are associated with RAO under controlled environmental conditions but ranges of mould-specific serum IgE levels overlapped too much between diseased and clinically healthy animals to be of any diagnostic value. Further studies are needed to assess whether IgE-mediated reactions contribute to the pathogenesis of RAO.

Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.