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

Universal Prefactor of Activated Conductivity in the Quantum Hall Effect

The prefactor of the activated dissipative conductivity in a plateau range of the quantum Hall effect is studied in the case of a long-range random potential. It is shown that due to long time it takes for an electron to drift along the perimeter of a large percolation cluster, phonons are able to maintain quasi-equilibrium inside the cluster. The saddle points separating such clusters may then be viewed as ballistic point contacts between electron reservoirs with different electrochemical potentials. The prefactor is universal and equal to 2$e^2/h$ at an integer filling factor $\nu$ and to 2$e^2/q^{2}h$ at $\nu=p/q$.Comment: 4 pages + 2 figures by reques

Investigation on the mechanisms govergning the robustness of self-compacting concrete at paste level

In spite of the many advantages, the use of self-compacting concrete (SCC) is currently widely limited to application in precast factories and situations in which external vibration would cause large difficulties. One of the main limitations is the higher sensitivity to small variations in mix proportions, material characteristics and procedures, also referred to as the lower robustness of SCC compared to vibrated concrete. This paper investigates the mechanisms governing the robustness at paste level. Phenomenological aspects are examined for a series of paste mixtures varying in water film thickness and superplasticizer-to-powder ratio. The impact of small variations in the water content on the early-age structural buildup and the robustness of the paste rheology is investigated using rotational and oscillating rheometry

Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds

In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compared with various geometric quantities such as volume, diameter and length of the shortest periodic geodesic of the manifolds. The deviation of low-lying eigenvalue spectra of manifolds converging to a cusped hyperbolic manifold from the asymptotic distribution has been measured by $\zeta-$ function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of cusped manifolds in section 2 is correcte

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

Finitely presented wreath products and double coset decompositions

We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X^2. On the one hand, this extends a result of G. Baumslag about standard wreath products; on the other hand, this provides nontrivial examples of finitely presented groups. For instance, we obtain two quasi-isometric finitely presented groups, one of which is torsion-free and the other has an infinite torsion subgroup. Motivated by the characterization above, we discuss the following question: which finitely generated groups can have a finitely generated subgroup with finitely many double cosets? The discussion involves properties related to the structure of maximal subgroups, and to the profinite topology.Comment: 21 pages; no figure. To appear in Geom. Dedicat

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

Global serum glycoform profiling for the investigation of dystroglycanopathies & Congenital Disorders of Glycosylation

The Congenital Disorders of Glycosylation (CDG) are an expanding group of genetic disorders which encompass a spectrum of glycosylation defects of protein and lipids, including N- & O-linked defects and among the latter are the muscular dystroglycanopathies (MD). Initial screening of CDG is usually based on the investigation of the glycoproteins transferrin, and/or apolipoprotein CIII. These biomarkers do not always detect complex or subtle defects present in older patients, therefore there is a need to investigate additional glycoproteins in some cases. We describe a sensitive 2D-Differential Gel Electrophoresis (DIGE) method that provides a global analysis of the serum glycoproteome. Patient samples from PMM2-CDG (n = 5), CDG-II (n = 7), MD and known complex N- & O-linked glycosylation defects (n = 3) were analysed by 2D DIGE. Using this technique we demonstrated characteristic changes in mass and charge in PMM2-CDG and in charge in CDG-II for α1-antitrypsin, α1-antichymotrypsin, α2-HS-glycoprotein, ceruloplasmin, and α1-acid glycoproteins 1&2. Analysis of the samples with known N- & O-linked defects identified a lower molecular weight glycoform of C1-esterase inhibitor that was not observed in the N-linked glycosylation disorders indicating the change is likely due to affected O-glycosylation. In addition, we could identify abnormal serum glycoproteins in LARGE and B3GALNT2-deficient muscular dystrophies. The results demonstrate that the glycoform pattern is varied for some CDG patients not all glycoproteins are consistently affected and analysis of more than one protein in complex cases is warranted. 2D DIGE is an ideal method to investigate the global glycoproteome and is a potentially powerful tool and secondary test for aiding the complex diagnosis and sub classification of CDG. The technique has further potential in monitoring patients for future treatment strategies. In an era of shifting emphasis from gel- to mass-spectral based proteomics techniques, we demonstrate that 2D-DIGE remains a powerful method for studying global changes in post-translational modifications of proteins

The littlest Higgs model and Higgs boson associated production with top quark pair at high energy linear e+e−e^{+}e^{-} collider

In the parameter space allowed by the electroweak precision measurement data, we consider the contributions of the new particles predicted by the littlest Higgs($LH$) model to the Higgs boson associated production with top quark pair in the future high energy linear $e^{+}e^{-}$ collider($ILC$). We find that the contributions mainly come from the new gauge bosons $Z_{H}$ and $B_{H}$. For reasonable values of the free parameters, the absolute value of the relative correction parameter $\delta\sigma/\sigma^{SM}$ can be significanly large, which might be observed in the future $ILC$ experiment with $\sqrt{S}=800GeV$.Comment: latex files, 13 pages, 3 figure