Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

A Combination Theorem for Metric Bundles

We define metric bundles/metric graph bundles which provide a purely topological/coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina-Feighn in the special case that the inclusions of the edge spaces into the vertex spaces are uniform coarsely surjective quasi-isometries. We prove the existence of quasi-isometric sections in this generality. Then we prove a combination theorem for metric (graph) bundles (including exact sequences of groups) that establishes sufficient conditions, particularly flaring, under which the metric bundles are hyperbolic. We use this to give examples of surface bundles over hyperbolic disks, whose universal cover is Gromov-hyperbolic. We also show that in typical situations, flaring is also a necessary condition.Comment: v3: Major revision: 56 pages 5 figures. Many details added. Characterization of convex cocompact subgroups of mapping class groups of surfaces with punctures in terms of relative hyperbolicity given v4: Final version incorporating referee comments: 63 pages 5 figures. To appear in Geom. Funct. Ana

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Non-Canonical NF-κB Activation and Abnormal B Cell Accumulation in Mice Expressing Ubiquitin Protein Ligase-Inactive c-IAP2

Loss of c-IAP2 ubiquitin ligase activity, which occurs in the lymphoma-causing c-IAP2/MALT1 fusion protein, activates non-canonical NF-κB signaling and results in B cell abnormalities characteristic of MALT lymphoma

Anosov representations: Domains of discontinuity and applications

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica

Regulation of the small regulatory RNA MicA by ribonuclease III: a target-dependent pathway

MicA is a trans-encoded small non-coding RNA, which downregulates porin-expression in stationary-phase. In this work, we focus on the role of endoribonucleases III and E on Salmonella typhimurium sRNA MicA regulation. RNase III is shown to regulate MicA in a target-coupled way, while RNase E is responsible for the control of free MicA levels in the cell. We purified both Salmonella enzymes and demonstrated that in vitro RNase III is only active over MicA when in complex with its targets (whether ompA or lamB mRNAs). In vivo, MicA is demonstrated to be cleaved by RNase III in a coupled way with ompA mRNA. On the other hand, RNase E is able to cleave unpaired MicA and does not show a marked dependence on its 5′ phosphorylation state. The main conclusion of this work is the existence of two independent pathways for MicA turnover. Each pathway involves a distinct endoribonuclease, having a different role in the context of the fine-tuned regulation of porin levels. Cleavage of MicA by RNase III in a target-dependent fashion, with the concomitant decay of the mRNA target, strongly resembles the eukaryotic RNAi system, where RNase III-like enzymes play a pivotal role

Definitions of quasiconformality

We establish that the infinitesimal “ H -definition” for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even in R n where we obtain that the “limsup” condition in the H -definition can be replaced by a “liminf” condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-arc surfaces is also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46582/1/222_2005_Article_BF01241122.pd