The first three anisotropy constants of nickel

The technique of ferromagnetic resonance at 23 GHz has been used to determine the first three anisotropy constants of pure Ni down to 4.2K. A temperature and orientation dependent linewidth has also been observed.     

Manifold preprocessing for laser‐induced breakdown spectroscopy under Mars conditions

Laser‐induced breakdown spectroscopy (LIBS) is currently being used onboard the Mars Science Laboratory rover Curiosity to predict elemental abundances in dust, rocks, and soils using a partial least squares regression model developed by the ChemCam team. Accuracy of that model is constrained by the number of samples needed in the calibration, which grows exponentially with the dimensionality of the data, a phenomenon known as the curse of dimensionality. LIBS data are very high dimensional, and the number of ground‐truth samples (i.e., standards) recorded with the ChemCam before departing for Mars was small compared with the dimensionality, so strategies to optimize prediction accuracy are needed. In this study, we first use an existing machine learning algorithm, locally linear embedding (LLE), to combat the curse of dimensionality by embedding the data into a low‐dimensional manifold subspace before regressing. LLE constructs its embedding by maintaining local neighborhood distances and discarding large global geodesic distances between samples, in an attempt to preserve the underlying geometric structure of the data. We also introduce a novel supervised version, LLE for regression (LLER), which takes into account the known chemical composition of the training data when embedding. LLER is shown to outperform traditional LLE when predicting most major elements. We show the effectiveness of both algorithms using three different LIBS datasets recorded under Mars‐like conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Final group topologies,Kac-Moody groups and Pontryagin duality

We study final group topologies and their relations to compactness properties. In particular, we are interested in situations where a colimit or direct limit is locally compact, a k _ω-space, or locally k _ω. As a first application, we show that unitary forms of complex Kac-Moody groups can be described as the colimit of an amalgam of subgroups (in the category of Hausdorff topological groups, and the category of k _ω-groups). Our second application concerns Pontryagin duality theory for the classes of almost metrizable topological abelian groups, resp., locally k _ω topological abelian groups, which are dual to each other. In particular, we explore the relations between countable projective limits of almost metrizable abelian groups and countable direct limits of locally k _ω abelian groups.