Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories

We generalize the $N_F=2$ Schwinger model on the lattice by adding a charged scalar field. In this so-called $\chi U\phi_2$ model the scalar field shields the fermion charge, and a neutral fermion, acquiring mass dynamically, is present in the spectrum. We study numerically the mass of this fermion at various large fixed values of the gauge coupling by varying the effective four-fermion coupling, and find an indication that its scaling behavior is the same as that of the fermion mass in the chiral Gross-Neveu model. This suggests that the $\chi U\phi_2$ model is in the same universality class as the Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary strong gauge coupling.Comment: 18 pages, LaTeX2e, requires packages rotating.sty and curves.sty from CTA

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

High STEAP1 expression is associated with improved outcome of Ewing's sarcoma patients

Background Ewing's sarcoma (ES) is the second most common bone or soft-tissue sarcoma in childhood and adolescence and features a high propensity to metastasize. The six-transmembrane epithelial antigen of the prostate 1 (STEAP1) is a membrane-bound mesenchymal stem cell marker highly expressed in ES. Here, we investigated the role of STEAP1 as an immunohistological marker for outcome prediction in patients with ES. Patients and methods Membranous STEAP1 immunoreactivity was analyzed using immunohistochemistry in 114 primary pre-chemotherapy ES of patients diagnosed from 1983 to 2010 and compared with clinical parameters and patient outcome. Median follow-up was 3.85 years (range 0.43-17.51). Results A total of 62.3% of the ES samples displayed detectable STEAP1 expression with predominant localization of the protein at the plasma membrane. High membranous STEAP1 immunoreactivity was found in 53.5%, which correlated with better overall survival (P=0.021). Accordingly, no or low membranous STEAP1 expression was identified as an independent risk factor in multivariate analysis (hazard ratio 2.65, P=0.036). Conclusion High membranous STEAP1 expression predicts improved outcome and may help to define a specific subgroup of ES patients, who might benefit from adapted therapy regimen

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

On the Whitehead spectrum of the circle

The seminal work of Waldhausen, Farrell and Jones, Igusa, and Weiss and Williams shows that the homotopy groups in low degrees of the space of homeomorphisms of a closed Riemannian manifold of negative sectional curvature can be expressed as a functor of the fundamental group of the manifold. To determine this functor, however, it remains to determine the homotopy groups of the topological Whitehead spectrum of the circle. The cyclotomic trace of B okstedt, Hsiang, and Madsen and a theorem of Dundas, in turn, lead to an expression for these homotopy groups in terms of the equivariant homotopy groups of the homotopy fiber of the map from the topological Hochschild T-spectrum of the sphere spectrum to that of the ring of integers induced by the Hurewicz map. We evaluate the latter homotopy groups, and hence, the homotopy groups of the topological Whitehead spectrum of the circle in low degrees. The result extends earlier work by Anderson and Hsiang and by Igusa and complements recent work by Grunewald, Klein, and Macko.Comment: 52 page

Higgs boson pair production process e+e−→ZHHe^+e^-\to ZHH in the littlest Higgs model at the ILC

The physics prospect at future linear $e^{+}e^{-}$ colliders for the study of the Higgs triple self-coupling via the process of $e^{+}e^{-}\to ZHH$ is investigated. In this paper, we calculate the contribution of the new particles predicted by the littlest Higgs model to the cross sections of this process in the future high energy $e^{+}e^{-}$ collider($ILC$). The results show that, in the favorable parameter spaces preferred by the electroweak precision, the deviation of the total cross sections from its $SM$ value varies from a few percent to tens percent, which may be detected at the future $ILC$ experiments with $\sqrt{s}$=500GeV.Comment: 13 pages,4 figure

Arterial microanatomy determines the success of energy-based renal denervation in controlling hypertension

Renal denervation (RDN) is a treatment option for patients with hypertension resistant to conventional therapy. Clinical trials have demonstrated variable benefit. To understand the determinants of successful clinical response to this treatment, we integrated porcine and computational models of intravascular radiofrequency RDN. Controlled single-electrode denervation resulted in ablation zone geometries that varied in arc, area, and depth, depending on the composition of the adjacent tissue substructure. Computational simulations predicted that delivered power density was influenced by tissue substructure, and peaked at the conductivity discontinuities between soft fatty adventitia and water-rich tissues (media, lymph nodes, etc.), not at the electrode-tissue interface. Electrode irrigation protected arterial wall tissue adjacent to the electrode by clearing heat that diffuses from within the tissue, without altering periarterial ablation. Seven days after multielectrode treatments, renal norepinephrine and blood pressure were reduced. Blood pressure reductions were correlated with the size-weighted number of degenerative nerves, implying that the effectiveness of the treatment in decreasing hypertension depends on the extent of nerve injury and ablation, which in turn are determined by the tissue microanatomy at the electrode site. These results may explain the variable patient response to RDN and suggest a path to more robust outcomes.National Institutes of Health (U.S.) (NIH grant R01 GM-49039

Proximity of Transmembrane Segments 5 and 8 of the Glutamate Transporter GLT-1 Inferred from Paired Cysteine Mutagenesis

BACKGROUND: GLT-1 is a glial glutamate transporter which maintains low synaptic concentrations of the excitatory neurotransmitter enabling efficient synaptic transmission. Based on the crystal structure of the bacterial homologue Glt(Ph), it has been proposed that the reentrant loop HP2, which connects transmembrane domains (TM) 7 and 8, moves to open and close access to the binding pocket from the extracellular medium. However the conformation change between TM5 and TM8 during the transport cycle is not clear yet. We used paired cysteine mutagenesis in conjunction with treatments with Copper(II)(1,10-Phenanthroline)(3) (CuPh), to verify the predicted proximity of residues located at these structural elements of GLT-1. METHODOLOGY/PRINCIPAL FINDINGS: To assess the proximity of transmembrane domain (TM) 5 relative to TM8 during transport by the glial glutamate transporter GLT-1/EAAT2, cysteine pairs were introduced at the extracellular ends of these structural elements. A complete inhibition of transport by Copper(II)(1,10-Phenanthroline)(3) is observed in the double mutants I295C/I463C and G297C/I463C, but not in the corresponding single mutants. Glutamate and potassium, both expected to increase the proportion of inward-facing transporters, significantly protected against the inhibition of transport activity of I295C/I463C and G297C/I463C by CuPh. Transport by the double mutants I295C/I463C and G297C/I463C also was inhibited by Cd(2+). CONCLUSIONS/SIGNIFICANCE: Our results suggest that TM5 (Ile-295, Gly-297) is in close proximity to TM8 (Ile-463) in the mammalian transporter, and that the spatial relationship between these domains is altered during the transport cycle