OPTIMAL SHAPE IN ELECTROMAGNETIC SCATTERING BY SMALL ASPHERICAL PARTICLES

We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.

A Note on the Use of Sum in the Logic of Proofs

The Logic of Proofs~LP, introduced by Artemov, encodes the same reasoning as the modal logic~S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application~$\cdot$, positive introspection~!, and sum~+) are sufficient to mimic provability concealed in S4~modality. While the first two operations go back to G{\"o}del, the exact role of~+ remained somewhat unclear. In particular, it was not known whether the other two operations are sufficient by themselves. We provide a positive answer to this question under a very weak restriction on the axiomatization of LP.

Passive-Active Geometric Calibration for View-Dependent Projections onto Arbitrary Surfaces

In this paper we present a hybrid technique for correcting distortions that appear when projecting images onto geometrically complex, colored and textured surfaces. It analyzes the optical flow that results from perspective distortions during motions of the observer and tries to use this information for computing the correct image warping. If this fails due to an unreliable optical flow, an accurate -but slower and visiblestructured light projection is automatically triggered. Together with an appropriate radiometric compensation, view-dependent content can be projected onto arbitrary everyday surfaces. An implementation mainly on the GPU ensures fast frame rates.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Geometric properties of the lung parenchyma after postnatal glucocorticoid treatment in rats

While glucocorticoid (GC) administration appears to be beneficial during the acute phase of treatment of neonates at risk of developing chronic lung disease, it is still not clear whether steroid application has an adverse long-term effect on the lung maturation. Thus, the goal of the present work was to analyze GC effects on the pulmonary structure in a rat model where dosage and timing of drug administration were adapted to the therapeutic situation in human neonatology. The animals received daily a maximum of 0.1 mg dexamethasone phosphate per kilogram body weight during the first 4 postnatal days. Investigations were performed at the light microscopic level by means of a digital image analysis system. While there were no differences in the lung architecture between experimental animals and controls on day 4, the earliest time point of observation, we found a widening of airspaces with a concomitant decrease in the alveolar surface area density, representing a loss of parenchymal complexity, on days 10 and 21 in treated rats. On days 36 and 60, however, no alterations in the pulmonary parenchyma could be detected in experimental animals. We conclude from these findings that the GC-induced initial inhibition of development (days 10 and 21) was completely reversed, so that a normal parenchymal architecture and also a normal alveolar surface area density were found in adult rats (days 36 and 60). From the results obtained using the regimen of GC administration described, mimicking more closely the steroid treatment in human neonatology, we conclude that the observed short-term adverse effects on lung development can be fully compensated until adult age.

Item Sum: A New Technique for Asking Quantitative Sensitive Questions

This article contributes to an ongoing debate about how to measure sensitive topics in population surveys. We propose a novel technique that can be applied to the measurement of quantitative sensitive variables: the item sum technique (IST). This method is closely related to the item count technique, which was developed for the measurement of dichotomous sensitive items. First, we provide a description of our new technique and discuss how data collected by the IST can be analyzed. Second, we present the results of a CATI survey on undeclared work in Germany, in which the IST has been applied. Using an experimental design, we compare the IST to direct questioning. Our empirical results indicate that the IST is a promising data-collection technique for sensitive questions. We conclude by discussing the limitations of the new technique and outlining possible improvements for future studies.