Sike B. Gahleitner/Hans G. Homfeldt (Hrsg.): Kinder und Jugendliche mit speziellem Versorgungsbedarf. Beispiele und Lösungswege für Kooperation der sozialen Dienste, Weinheim und Basel: Beltz-Juventa 2012 (290 S.) [Rezension]

Rezension von: Sike B. Gahleitner/Hans G. Homfeldt (Hrsg.): Kinder und Jugendliche mit speziellem Versorgungsbedarf. Beispiele und Lösungswege für Kooperation der sozialen Dienste, Weinheim und Basel: Beltz-Juventa 2012(290 S.; ISBN 978-3-7799-2263-6

The dynamics of crack patterns in soil induced by desiccation

Many soil types develop cracks due to desiccation. The resulting crack patterns were simulated with the help of a network of springs, representing the breaking material. A spring breaks if the tensile stress on it exceeds a threshold. Based on existing models in the literature a numerical model was developed. It was used to study the time evolution of cracking and to investigate the nal crack pattern. It came out, that the model repro- duces some phenomena which can be observed in natural crack patterns (90 degree angles of intersections, dynamics of emerging cracks). Two parameters of the model - the disorder in the distribution of stress thresholds for the individual springs and a slipping threshold (resembling friction) - were varied and their impact on the crack pattern was studied. It was found that friction induces a characteristic scale. Varying disorder, a continuous transition from loop-like closed cracks (loops) to a system of not interconnected cracks was observed. The number of loops in the topology of the crack pattern, was introduced as an order parameter. Besides the theoretical part, an experiment was carried out. A bentonite-sand-water mixture was prepared as a layer on a glass plate and dried at room temperature. As a result of drying crack patterns developed. These were recorded by a digital camera. Binary pictures were obtained and the number of loops in the crack patterns of the completely dried mixtures counted. Varying the mass ratio of bentonite to sand a similar transition sas in the model was observed

Sliced Wasserstein Distance for Learning Gaussian Mixture Models

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which could be arbitrarily worse than the optimal solution. Inspired by the relationship between the negative log-likelihood function and the Kullback-Leibler (KL) divergence, we propose an alternative formulation for estimating the GMM parameters using the sliced Wasserstein distance, which gives rise to a new algorithm. Specifically, we propose minimizing the sliced-Wasserstein distance between the mixture model and the data distribution with respect to the GMM parameters. In contrast to the KL-divergence, the energy landscape for the sliced-Wasserstein distance is more well-behaved and therefore more suitable for a stochastic gradient descent scheme to obtain the optimal GMM parameters. We show that our formulation results in parameter estimates that are more robust to random initializations and demonstrate that it can estimate high-dimensional data distributions more faithfully than the EM algorithm

Descriptive characterisation of the variational Henstock-Kurzweil-Stieltjes integral and applications

We derive a descriptive characterisation of the vector-valued variational Henstock-Kurzweil-Stieltjes integral extending and improving previous results. We also give several applications of our characterisation, e.g., to the recover of a function from a relative derivative, the characterisation of Banach spaces with the Radon-Nikodým property and to the study of certain normed algebras of differentiable functions on compact plane sets

Capturing Vacuum Fluctuations and Photon Correlations in Cavity Quantum Electrodynamics with Multi-Trajectory Ehrenfest Dynamics

We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehrenfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field, through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum-classical (mean field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems