Low rank tensor recovery via iterative hard thresholding

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank matrix recovery is already well-developed, only few contributions on the low rank tensor recovery problem are available so far. In this paper, we introduce versions of the iterative hard thresholding algorithm for several tensor decompositions, namely the higher order singular value decomposition (HOSVD), the tensor train format (TT), and the general hierarchical Tucker decomposition (HT). We provide a partial convergence result for these algorithms which is based on a variant of the restricted isometry property of the measurement operator adapted to the tensor decomposition at hand that induces a corresponding notion of tensor rank. We show that subgaussian measurement ensembles satisfy the tensor restricted isometry property with high probability under a certain almost optimal bound on the number of measurements which depends on the corresponding tensor format. These bounds are extended to partial Fourier maps combined with random sign flips of the tensor entries. Finally, we illustrate the performance of iterative hard thresholding methods for tensor recovery via numerical experiments where we consider recovery from Gaussian random measurements, tensor completion (recovery of missing entries), and Fourier measurements for third order tensors.Comment: 34 page

Wohlfahrts- und Verteilungseffekte eines allgemeinen Freibetrags bei den Sozialabgaben (Welfare and distribution effects of a general fixed allowance for social insurance contributions)

"The paper simulates the labor market impact of a fixed allowance for social insurance contributions. Based on a discrete choice labor supply model estimated using data from the German Socio-Economic Panel, we evaluate household utility changes triggered by the reform, including behavioral responses. Directly the reform raises individual welfare throughout. However, refinancing its substantial fiscal costs through a general consumption tax reduces aggregate labor supply and household utility levels, with progressive absolute losses. A poll tax preserves the immediate positive labor supply effect, but reverses entirely the benefits from the allowance except for households in the lowest income decile." (Author's abstract, IAB-Doku) ((en))Verteilungseffekte, Lohnsubvention, Beschäftigungseffekte, Sozialabgaben, Freibetrag - Finanzierung, Arbeitskräfteangebot - Modell, Einkommenseffekte, Niedrigeinkommen, Erwerbsverhalten, Arbeitsvolumen, Arbeitszeitwunsch, Steuererhöhung

Workfare: Eine wirksame Alternative zum Kombilohn

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The 400d Galaxy Cluster Survey weak lensing programme: II: Weak lensing study of seven clusters with MMT/Megacam

Evolution in the mass function of galaxy clusters sensitively traces both the expansion history of the Universe and cosmological structure formation. Robust cluster mass determinations are a key ingredient for a reliable measurement of this evolution, especially at high redshift. Weak gravitational lensing is a promising tool for, on average, unbiased mass estimates. This weak lensing project aims at measuring reliable weak lensing masses for a complete X-ray selected sample of 36 high redshift (0.35<z<0.9) clusters. The goal of this paper is to demonstrate the robustness of the methodology against commonly encountered problems, including pure instrumental effects, the presence of bright (8--9 mag) stars close to the cluster centre, ground based measurements of high-z (z~0.8) clusters, and the presence of massive unrelated structures along the line-sight. We select a subsample of seven clusters observed with MMT/Megacam. Instrumental effects are checked in detail by cross-comparison with an archival CFHT/MegaCam observation. We derive mass estimates for seven clusters by modelling the tangential shear with an NFW profile, in two cases with multiple components to account for projected structures in the line-of-sight. We firmly detect lensing signals from all seven clusters at more than $3.5\sigma$ and determine their masses, ranging from $10^{14} M_{\odot}$ to $10^{15} M_{\odot}$, despite the presence of nearby bright stars. We retrieve the lensing signal of more than one cluster in the CL 1701+6414 field, while apparently observing CL 1701+6414 through a massive foreground filament. We also find a multi-peaked shear signal in CL 1641+4001. Shear structures measured in the MMT and CFHT images of CL 1701+6414 are highly correlated.Comment: Accepted for publication in Astronomy & Astrophysics; A&A 546, A7

SQUIRRELnovo : de novo design of a PPARalpha agonist by bioisosteric replacement

Shape complementarity is a compulsory condition for molecular recognition. In our 3D ligand-based virtual screening approach called SQUIRREL, we combine shape-based rigid body alignment with fuzzy pharmacophore scoring. Retrospective validation studies demonstrate the superiority of methods which combine both shape and pharmacophore information on the family of peroxisome proliferator-activated receptors (PPARs). We demonstrate the real-life applicability of SQUIRREL by a prospective virtual screening study, where a potent PPARalpha agonist with an EC50 of 44 nM and 100-fold selectivity against PPARgamma has been identified..

Workfare – praktikabel und gerecht

Dieses Modell stellt das Niveau des Arbeitslosengeldes II nicht in Frage, macht aber seine Gewährung von einer Gegenleistung in Form von Workfare (d.h. öffentlich organisierter Vollzeitbeschäftigung) abhängig. Wer das Workfare-Angebot nicht annimmt, muss aber auf sein Arbeitslosengeld II verzichten.Workfare, Arbeitslosigkeit, Ungelernte Arbeitskräfte, Niedriglohn, Deutschland, Kombilohn