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

Consensus clustering in complex networks

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on the specific random seeds, initial conditions and tie-break rules adopted for their execution. Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Here we show that consensus clustering can be combined with any existing method in a self-consistent way, enhancing considerably both the stability and the accuracy of the resulting partitions. This framework is also particularly suitable to monitor the evolution of community structure in temporal networks. An application of consensus clustering to a large citation network of physics papers demonstrates its capability to keep track of the birth, death and diversification of topics.Comment: 11 pages, 12 figures. Published in Scientific Report