Multiple noncommutative tori and Hopf algebras

We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.Comment: 18 pages; AMSLaTeX (major revision, the construction of dual rewritten using approach of multiplier Hopf algebras, references added

Ecological and functional optimization of the pretreatment process for plasma based coatings of cutting tools

Increasing demands in machining of high-tech materials and dry machining lead to higher thermal and mechanical loads on cutting tools. In response to these challenges, enhanced coating solutions are applied to increase performance and life of cutting tools. However, during the production process the cemented carbide substrates are contaminated with grinding oils and residues of organic material. For the subsequent physical vapor deposition (PVD) coating process an intensive and high-quality cleaning process is necessary. In this contribution, plasma electrolytic polishing (PEP) is used as a novel alternative to conventional ecologically harmful cleaning baths. Apart from the ecological advantage, the surface of the substrate can be optimized with regard to the coating adhesion. To examine the performance of the different cleaning processes, machining tests were performed at the IWF to evaluate the layer adhesion and tool life of the tools

'Schwinger Model' on the Fuzzy Sphere

In this paper, we construct a model of spinor fields interacting with specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this 'Schwinger model'. In constructing the theory of gauge fields interacting with spinors on fuzzy sphere, we take the approach that the Dirac operator $D_q$ on q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on fuzzy sphere. This introduces interaction between spinors and specific one parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators $D_q$ and $D$ alone. Using the path integral method, we have calculated the $2n-$point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys. Lett.

A high-finesse Fabry-Perot cavity with a frequency-doubled green laser for precision Compton polarimetry at Jefferson Lab

A high-finesse Fabry-Perot cavity with a frequency-doubled continuous wave green laser (532~nm) has been built and installed in Hall A of Jefferson Lab for high precision Compton polarimetry. The infrared (1064~nm) beam from a ytterbium-doped fiber amplifier seeded by a Nd:YAG nonplanar ring oscillator laser is frequency doubled in a single-pass periodically poled MgO:LiNbO$_{3}$ crystal. The maximum achieved green power at 5 W IR pump power is 1.74 W with a total conversion efficiency of 34.8\%. The green beam is injected into the optical resonant cavity and enhanced up to 3.7~kW with a corresponding enhancement of 3800. The polarization transfer function has been measured in order to determine the intra-cavity circular laser polarization within a measurement uncertainty of 0.7\%. The PREx experiment at Jefferson Lab used this system for the first time and achieved 1.0\% precision in polarization measurements of an electron beam with energy and current of 1.0~GeV and 50~$\mu$A.Comment: 20 pages, 22 figures, revised version of arXiv:1601.00251v1, submitted to NIM

Spin Foams and Noncommutative Geometry

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure

Viscoelastic properties of differentiating blood cells are fate- and function-dependent

This is the final version of the article. Available from the publisher via the DOI in this record.Although cellular mechanical properties are known to alter during stem cell differentiation, understanding of the functional relevance of such alterations is incomplete. Here, we show that during the course of differentiation of human myeloid precursor cells into three different lineages, the cells alter their viscoelastic properties, measured using an optical stretcher, to suit their ultimate fate and function. Myeloid cells circulating in blood have to be advected through constrictions in blood vessels, engendering the need for compliance at short time-scales (minutes), compared to undifferentiated cells. These findings suggest that reduction in steady-state viscosity is a physiological adaptation for enhanced migration through tissues. Our results indicate that the material properties of cells define their function, can be used as a cell differentiation marker and could serve as target for novel therapies.Funding: The authors acknowledge financial support by the Cambridge Commonwealth Trust (to AEE; http://www.cambridgetrusts.org), the Medical Research Council (to KC and JG; grant number: 94185; http://www.mrc.ac.uk), the Human Frontier Science Program (to GW and JG; grant number: RGP0015/2009-C; http:// www.hfsp.org) and the European Research Council (to JG; grant number: 282060; http://erc.europa.eu)

The Index of (White) Noises and their Product Systems

(See detailed abstract in the article.) We single out the correct class of spatial product systems (and the spatial endomorphism semigroups with which the product systems are associated) that allows the most far reaching analogy in their classifiaction when compared with Arveson systems. The main differences are that mere existence of a unit is not it sufficient: The unit must be CENTRAL. And the tensor product under which the index is additive is not available for product systems of Hilbert modules. It must be replaced by a new product that even for Arveson systems need not coincide with the tensor product

Recurrent EZH1 mutations are a second hit in autonomous thyroid adenomas

Autonomous thyroid adenomas (ATAs) are a frequent cause of hyperthyroidism. Mutations in the genes encoding the TSH receptor (TSHR) or the Gs protein alpha subunit (GNAS) are found in approximately 70% of ATAs. The involvement of other genes and the pathogenesis of the remaining cases are presently unknown. Here, we performed whole-exome sequencing in 19 ATAs that were paired with normal DNA samples and identified a recurrent hot-spot mutation (c.1712A>G; p.Gln571Arg) in the enhancer of zeste homolog 1 (EZH1) gene, which codes for a catalytic subunit of the polycomb complex. Targeted screening in an independent cohort confirmed that this mutation occurs with high frequency (27%) in ATAs. EZH1 mutations were strongly associated with known (TSHR, GNAS) or presumed (adenylate cyclase 9 [ADCY9]) alterations in cAMP pathway genes. Furthermore, functional studies revealed that the p.Gln571Arg EZH1 mutation caused increased histone H3 trimethylation and increased proliferation of thyroid cells. In summary, this study revealed that a hot-spot mutation in EZH1 is the second most frequent genetic alteration in ATAs. The association between EZH1 and TSHR mutations suggests a 2-hit model for the pathogenesis of these tumors, whereby constitutive activation of the cAMP pathway and EZH1 mutations cooperate to induce the hyperproliferation of thyroid cells.IZKF Wurzburg [B-281]; ERA-NET E-Rare [01GM1407B]; Deutsche KrebshilfeDeutsche Krebshilfe [109994]; Wilhelm Sander Stiftung [2013.010.1]We wish to thank Eileen Bosenberg, Bianca Klupfel, and Ines Elsner for technical support and Ulrike Zabel for DNA cloning. This study was partially supported by grants from the IZKF Wurzburg (B-281, to DC and MF); the ERA-NET E-Rare (01GM1407B, to MF and DC); the Deutsche Krebshilfe (109994, to ME); and the Wilhelm Sander Stiftung (project 2013.010.1, to RP)