The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

A2163: Merger events in the hottest Abell galaxy cluster II. Subcluster accretion with galaxy-gas separation

Located at z = 0.203, A2163 is a rich galaxy cluster with an intra-cluster medium (ICM) that exhibits extraordinary properties, including an exceptionally high X-ray luminosity, average temperature, and a powerful and extended radio halo. The irregular and complex morphology of its gas and galaxy structure suggests that this cluster has recently undergone major merger events that involve two or more cluster components. In this paper, we study the gas structure and dynamics by means of spectral-imaging analysis of X-ray data obtained from XMM-Newton and Chandra observations. From the evidence of a cold front, we infer the westward motion of a cool core across the E-W elongated atmosphere of the main cluster A2163-A. Located close to a galaxy over-density, this gas 'bullet' appears to have been spatially separated from its galaxy (and presumably dark matter component) as a result of high-velocity accretion. From gas brightness and temperature profile analysis performed in two opposite regions of the main cluster, we show that the ICM has been adiabatically compressed behind the crossing 'bullet' possibly because of shock heating, leading to a strong departure of the ICM from hydrostatic equilibrium in this region. Assuming that the mass estimated from the Yx proxy best indicates the overall mass of the system and that the western cluster sector is in approximate hydrostatic equilibrium before subcluster accretion, we infer a merger scenario between two subunits of mass ratio 1:4, leading to a present total system mass of M500 $\propto 1.9 \times 1015 M_{\odot}$. The exceptional properties of A2163 present various similarities with those of 1E0657-56, the so-called 'bullet-cluster'. These similarities are likely to be related to a comparable merger scenario.Comment: A&A, in pres

Transcriptomes of the B and T lineages compared by multiplatform microarray profiling

T and B lymphocytes are developmentally and functionally related cells of the immune system, representing the two major branches of adaptive immunity. Although originating from a common precursor, they play very different roles: T cells contribute to and drive cell-mediated immunity, whereas B cells secrete Abs. Because of their functional importance and well-characterized differentiation pathways, T and B lymphocytes are ideal cell types with which to understand how functional differences are encoded at the transcriptional level. Although there has been a great deal of interest in defining regulatory factors that distinguish T and B cells, a truly genomewide view of the transcriptional differences between these two cells types has not yet been taken. To obtain a more global perspective of the transcriptional differences underlying T and B cells, we exploited the statistical power of combinatorial profiling on different microarray platforms, and the breadth of the Immunological Genome Project gene expression database, to generate robust differential signatures. We find that differential expression in T and B cells is pervasive, with the majority of transcripts showing statistically significant differences. These distinguishing characteristics are acquired gradually, through all stages of B and T differentiation. In contrast, very few T versus B signature genes are uniquely expressed in these lineages, but are shared throughout immune cells.National Institute of Allergy and Infectious Diseases (U.S.) (National Institutes of Health (R24 AI072073

Phase transition curves for mesoscopic superconducting samples

We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an asymptotic formula for the ground state of the Schr\"odinger equation in the presence of large applied flux. The expansion is shown to be sensitive to the smoothness of the domain. The theoretical results are compared to recent experiments.Comment: 8 pages, 1 figur

A refined stable restriction theorem for vector bundles on quadric threefolds

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a closed subset of codimension at least 2 of the dual projective 4-space, and we explicitly describe the bundles E which do not enjoy this property. This refines a restriction theorem of Ein and Sols [Nagoya Math. J. 96, 11-22 (1984)] in the same way the main result of Coanda [J. reine angew. Math. 428, 97-110 (1992)] refines the restriction theorem of Barth [Math. Ann. 226, 125-150 (1977)].Comment: Ann. Mat. Pura Appl. 201

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

Influence of the confinement geometry on surface superconductivity

The nucleation field for surface superconductivity, $H_{c3}$, depends on the geometrical shape of the mesoscopic superconducting sample and is substantially enhanced with decreasing sample size. As an example we studied circular, square, triangular and wedge shaped disks. For the wedge the nucleation field diverges as $H_{c3}/H_{c2}=\sqrt{3}/\alpha$ with decreasing angle ($\alpha$) of the wedge, where $H_{c2}$ is the bulk upper critical field.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev.

Dilation of the Giant Vortex State in a Mesoscopic Superconducting Loop

We have experimentally investigated the magnetisation of a mesoscopic aluminum loop at temperatures well below the superconducting transition temperature $T_{c}$. The flux quantisation of the superconducting loop was investigated with a $\mu$-Hall magnetometer in magnetic field intensities between $\pm 100 {Gauss}$. The magnetic field intensity periodicity observed in the magnetization measurements is expected to take integer values of the superconducting flux quanta $\Phi_{0}=h/2e$. A closer inspection of the periodicity, however, reveal a sub flux quantum shift. This fine structure we interpret as a consequence of a so called giant vortex state nucleating towards either the inner or the outer side of the loop. These findings are in agreement with recent theoretical reports.Comment: 12 pages, 5 figures. Accepted for publication in Phys. Rev.