Ventrales femoroacetabuläres Impingement nach geheilter Schenkelhalsfraktur

Zusammenfassung: Fragestellung.: Darstellung des ventralen femoroacetabulären Impingements (VFAI) als Ursache persistierender schmerzhafter Bewegungseinschränkungen und fortschreitender Gelenkschädigung nach geheilter Schenkelhalsfraktur sowie der Ergebnisse nach operativer Therapie des VFAI. Methodik.: Bei 11Patienten wurde ein VFAI mit bewegungs- und belastungsabhängigen Leistenschmerzen nach in Retrotorsion geheilter Schenkelhalsfraktur vermutet und nativröntgenologisch sowie mit radialer Arthro-MRT-Untersuchung bestätigt. Mit chirurgischer (Sub-)Luxation des Hüftgelenks wurde das Impingement offen überprüft und durch Wiederherstellung der Kontur des anterioren Übergangs zwischen Femurkopf und Schenkelhals beseitigt. Ergebnisse.: Bei sämtlichen Patienten zeigte sich eine Abflachung der Kontur des ventralen Kopf-Hals-Übergangs und ein dadurch hervorgerufenes Cam-Impingement mit konsekutiver Schädigung des pfannenrandnahen acetabulären Knorpels. Bei der Nachuntersuchung 5Jahre postoperativ fand sich eine deutliche Besserung der Symptomatik ohne Zunahme der Gelenkschädigung. Schlussfolgerung.: Bei chronischen Beschwerden nach geheilter Schenkelhalsfraktur ohne Kopfnekrose ist an die Möglichkeit eines VFAI durch Retrotorsion des Kopfes gegenüber dem Hals zu denken. Die durch VFAI hervorgerufene Symptomatik lässt sich durch chirurgische Optimierung des Kopf-Hals-Offset längerfristig verbessern. Ein bereits entstandener Gelenkschaden lässt sich allerdings kaum angehen. Eine Schenkelhalsfraktur sollte anatomisch reponiert werden, um der Arthroseentwicklung vorzubeuge

A study of blow-ups in the Keller-Segel model of chemotaxis

We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then compared with analytical predictions regarding formation and interaction of singularities obtained via analysis of the stochastic differential equations associated with the Keller-Segel model

On double Hurwitz numbers in genus 0

We study double Hurwitz numbers in genus zero counting the number of covers \CP^1\to\CP^1 with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise polynomials in the multiplicities of the preimages of the branching points. We describe the partition of the parameter space into polynomiality domains, called chambers, and provide an expression for the difference of two such polynomials for two neighboring chambers. Besides, we provide an explicit formula for the polynomial in a certain chamber called totally negative, which enables us to calculate double Hurwitz numbers in any given chamber as the polynomial for the totally negative chamber plus the sum of the differences between the neighboring polynomials along a path connecting the totally negative chamber with the given one.Comment: 17 pages, 3 figure

Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers

For all nonnegative integers n, the Franel numbers are defined as $$f_n=\sum_{k=0}^n {n\choose k}^3.$$ We confirm two conjectures of Z.-W. Sun on congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0 \pmod{2n^2}, \sum_{k=0}^{p-1}(3k+2)(-1)^k f_k &\equiv 2p^2 (2^p-1)^2 \pmod{p^5}, where n is a positive integer and p>3 is a prime.Comment: 8 pages, minor changes, to appear in Integral Transforms Spec. Func

Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes

Information-theoretic principles for learning and acting have been proposed to solve particular classes of Markov Decision Problems. Mathematically, such approaches are governed by a variational free energy principle and allow solving MDP planning problems with information-processing constraints expressed in terms of a Kullback-Leibler divergence with respect to a reference distribution. Here we consider a generalization of such MDP planners by taking model uncertainty into account. As model uncertainty can also be formalized as an information-processing constraint, we can derive a unified solution from a single generalized variational principle. We provide a generalized value iteration scheme together with a convergence proof. As limit cases, this generalized scheme includes standard value iteration with a known model, Bayesian MDP planning, and robust planning. We demonstrate the benefits of this approach in a grid world simulation.Comment: 16 pages, 3 figure

Extreme State Aggregation Beyond MDPs

We consider a Reinforcement Learning setup where an agent interacts with an environment in observation-reward-action cycles without any (esp.\ MDP) assumptions on the environment. State aggregation and more generally feature reinforcement learning is concerned with mapping histories/raw-states to reduced/aggregated states. The idea behind both is that the resulting reduced process (approximately) forms a small stationary finite-state MDP, which can then be efficiently solved or learnt. We considerably generalize existing aggregation results by showing that even if the reduced process is not an MDP, the (q-)value functions and (optimal) policies of an associated MDP with same state-space size solve the original problem, as long as the solution can approximately be represented as a function of the reduced states. This implies an upper bound on the required state space size that holds uniformly for all RL problems. It may also explain why RL algorithms designed for MDPs sometimes perform well beyond MDPs.Comment: 28 LaTeX pages. 8 Theorem

The Influence of Specimen Thickness on the High Temperature Corrosion Behavior of CMSX-4 during Thermal-Cycling Exposure

CMSX-4 is a single-crystalline Ni-base superalloy designed to be used at very high temperatures and high mechanical loadings. Its excellent corrosion resistance is due to external alumina-scale formation, which however can become less protective under thermal-cycling conditions. The metallic substrate in combination with its superficial oxide scale has to be considered as a composite suffering high stresses. Factors like different coefficients of thermal expansion between oxide and substrate during temperature changes or growing stresses affect the integrity of the oxide scale. This must also be strongly influenced by the thickness of the oxide scale and the substrate as well as the ability to relief such stresses, e.g., by creep deformation. In order to quantify these effects, thin-walled specimens of different thickness (t = 100500 lm) were prepared. Discontinuous measurements of their mass changes were carried out under thermal-cycling conditions at a hot dwell temperature of 1100 C up to 300 thermal cycles. Thin-walled specimens revealed a much lower oxide-spallation rate compared to thick-walled specimens, while thinwalled specimens might show a premature depletion of scale-forming elements. In order to determine which of these competetive factor is more detrimental in terms of a component’s lifetime, the degradation by internal precipitation was studied using scanning electron microscopy (SEM) in combination with energy-dispersive X-ray spectroscopy (EDS). Additionally, a recently developed statistical spallation model was applied to experimental data [D. Poquillon and D. Monceau, Oxidation of Metals, 59, 409–431 (2003)]. The model describes the overall mass change by oxide scale spallation during thermal cycling exposure and is a useful simulation tool for oxide scale spallation processes accounting for variations in the specimen geometry. The evolution of the net-mass change vs. the number of thermal cycles seems to be strongly dependent on the sample thickness