Asymptotic linear expansion of regularized M-estimators

Annals of the Institute of Statistical Mathematics - Parametric high-dimensional regression requires regularization terms to get interpretable models. The respective estimators correspond to...     

General Coorbit Space Theory for Quasi-Banach Spaces and Inhomogeneous Function Spaces with Variable Smoothness and Integrability

In this paper we propose a general coorbit space theory suitable to define coorbits of quasi-Banach spaces using an abstract continuous frame, indexed by a locally compact Hausdorff space, and an associated generalized voice transform. The proposed theory realizes a further step in the development of a universal abstract theory towards various function spaces and their atomic decompositions which has been initiated by Feichtinger and Gröchenig in the late 1980s. We combine the recent approaches in Rauhut and Ullrich (J Funct Anal 260(11):3299–3362, 2011) and Rauhut (Stud Math 180(3):237–253, 2007) to identify, in particular, various inhomogeneous (quasi-Banach) spaces of Besov–Lizorkin–Triebel type. To prove the potential of our new theory we apply it to spaces with variable smoothness and integrability which have attracted significant interest in the last 10 years. From the abstract discretization machinery we obtain atomic decompositions as well as wavelet frame isomorphisms for these spaces.     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.     

Transcranial direct current stimulation of the prefrontal cortex modulates working memory performance: combined behavioural and electrophysiological evidence

Background  

Transcranial direct current stimulation (tDCS) is a technique that can systematically modify behaviour by inducing changes in the underlying brain function. In order to better understand the neuromodulatory effect of tDCS, the present study examined the impact of tDCS on performance in a working memory (WM) task and its underlying neural activity. In two experimental sessions, participants performed a letter two-back WM task after sham and either anodal or cathodal tDCS over the left dorsolateral prefrontal cortex (DLPFC).     

Synthesis and Hydrogen-Bond Patterns of Aryl-Group Substituted Silanediols and -triols from Alkoxy- and Chlorosilanes

Organosilanols typically show a high condensation tendency and only exist as stable isolable molecules under very specific steric and electronic conditions at the silicon atom. In the present work, various novel representatives of this class of compounds were synthesized by hydrolysis of alkoxy- or chlorosilanes. Phenyl, 1-naphthyl, and 9-phenanthrenyl substituents at the silicon atom were applied to systematically study the influence of the aromatic substituents on the structure and reactivity of the compounds. Chemical shifts in ²⁹Si NMR spectroscopy in solution, correlated well with the expected electronic situation induced by the substitution pattern on the Si atom. ¹H NMR studies allowed the detection of strong intermolecular hydrogen bonds. Single-crystal X-ray structures of the alkoxides and the chlorosilanes are dominated by π-π interactions of the aromatic systems, which are substituted by strong hydrogen bonding interactions representing various structural motifs in the respective silanol structures.     

On an extreme class of real interpolation spaces

We investigate the limit class of interpolation spaces that comes up by the choice θ=0 in the definition of the real method. These spaces arise naturally interpolating by the J-method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ=1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.