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Estimating summary functionals in multistate models with an application to hospital infection data

Inhomogeneous Markov chains are a relevant framework for analysing event histories. The fundamental estimator in the presence of incompletely observed data is the Nelson-Aalen estimator of the multivariate cumulative hazards. It may be summarised in terms of probability estimates via the empirical transition matrix. The empirical transition matrix has only slowly entered applications, one reason being previous lack of software. In a number of applications, further summary measures are desired. We illustrate how they may be computed from the empirical transition matrix and why bootstrapping their variance works. In contrast, computing such summaries outside the present framework has typically led to biased results. As an example, we consider in more detail hospital stay following infectious complication. This summary quantity is often considered by clinical decision makers, but reliable estimates require modelling the timing of infection as in the present set-up. In this context, we also derive new summary measures that further distinguish between patients discharged and patients deceased.     

A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Given a domain Ω of class C ^k,1, k ∈ ℕ, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of in the sense that (∂/∂x _n )α(x′, 0) = − N(x′) and that still is of class C ^k,1. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class C ^k,1. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.     

Cavity formation at indium impurities in bcc metals

The defect formation in the bcc metals W and Mo above annealing stage III and the influence of rare gases on this process were investigated by means of the perturbed angular correlation technique using¹¹¹In as radioactive probe. In both metals a relatively high electric field gradient (EFG) could be observed at the indium site, characterized by the quadrupole interaction frequencies υ_Q=263 MHz, ν=0 and υ_Q=220 MHz, ν≈0.15 for W and Mo, respectively. The observations are assigned to the growth of threedimensional vacancy clusters at the probe atoms with the indium atoms situated in the inner surface of this cavities, thus experiencing the corresponding surface EFG.     

Measurement of the G asymmetry for the γp↦Nπ channels in the Δ(1232) resonance region

The G asymmetry of the γp↦Nπ reaction has been measured for the first time for E_γ = 340±14 MeV. This observable, for which very scarce published data exist, plays an important role to disentangle the contributions of the various nucleon resonances. The experiment, performed at the Mainz microtron MAMI, used a 4π-detector system, a linearly polarized, tagged photon beam, and a longitudinally polarized proton target.     

Mechanistic Insights into the Post‐Cyclization Isomerization in Gold‐Catalyzed 7‐exo‐dig‐Hydroarylations

The subsequent double‐bond isomerization in the synthesis of dibenzocycloheptenes and their heteroaromatic analogues was investigated. In the case of biphenyls, a basic additive completely prevented an isomerization to the thermodynamic product. With electron‐rich intramolecular heteroaromatic nucleophiles, the isomerization was still observed, but the kinetic product can be obtained by careful control of the reaction times in most cases. Mechanistic studies demonstrated that a slow isomerization is also possible with the gold catalyst at elevated temperatures, but much faster isomerization rates were observed with acidic additives. An observed initiation period for the gold‐catalyzed isomerization indicates that not the homogenous catalyst, but a decomposition product of it may be the catalytically active species.