Parabolic groups acting on one-dimensional compact spaces

Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of 1-dimensional connected boundaries. We get that any non-torsion infinite f.g. group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point. For boundaries homeomorphic to a Sierpinski carpet or a 2-sphere, the only maximal parabolic subgroups allowed are virtual surface groups (hyperbolic, or virtually $\mathbb{Z} + \mathbb{Z}$).Comment: 10 pages. Added a precision on local connectedness for Lemma 2.3, thanks to B. Bowditc

Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance $n^\epsilon$. Their rate is evaluated via Euler characteristic arguments and their distance using $\mathbb{Z}_2$-systolic geometry. This construction answers a queston of Z\'emor, who asked whether homological codes with such parameters could exist at all.Comment: 21 page

Qubit-Qutrit Separability-Probability Ratios

Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional hyperarea of the (separable and nonseparable) N x N density matrices, based on the Bures (minimal monotone) metric -- and also their analogous formulas (quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same seven billion well-distributed (``low-discrepancy'') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-six (rank-five) density matrices. The (rank-six) separability probabilities obtained based on the 35-dimensional volumes appear to be -- independently of the metric (each of the seven inducing Haar measure) employed -- twice as large as those (rank-five ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last paragraph presenting qubit-qutrit probability ratios disaggregated by the two distinct forms of partial transpositio

The K-theoretic Farrell-Jones Conjecture for hyperbolic groups

We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.Comment: 33 pages; final version; to appear in Invent. Mat

The longitude problem from the 1700s to today: An international and general education physics course

For instructors wishing to use physics as part of an international or general education course, the framework for a course based on the “longitude problem” from the 1700s is described. The longitude problem is teeming with basic principles of physics and astronomy, which makes it ideal for a non-science-major-based college-level course. This paper summarizes the longitude problem in the context of conceptual physics and astronomy and outlines an appropriate curriculum. Specifics on teaching such a course in London, as part of an international studies program, are discussed

Integrin α5β1 Function Is Regulated by XGIPC/kermit2 Mediated Endocytosis during Xenopus laevis Gastrulation

During Xenopus gastrulation α5β1 integrin function is modulated in a temporally and spatially restricted manner, however, the regulatory mechanisms behind this regulation remain uncharacterized. Here we report that XGIPC/kermit2 binds to the cytoplasmic domain of the α5 subunit and regulates the activity of α5β1 integrin. The interaction of kermit2 with α5β1 is essential for fibronectin (FN) matrix assembly during the early stages of gastrulation. We further demonstrate that kermit2 regulates α5β1 integrin endocytosis downstream of activin signaling. Inhibition of kermit2 function impairs cell migration but not adhesion to FN substrates indicating that integrin recycling is essential for mesoderm cell migration. Furthermore, we find that the α5β1 integrin is colocalized with kermit2 and Rab 21 in embryonic and XTC cells. These data support a model where region specific mesoderm induction acts through kermit2 to regulate the temporally and spatially restricted changes in adhesive properties of the α5β1 integrin through receptor endocytosis

Rate-dependent Ca2+ signalling underlying the force-frequency response in rat ventricular myocytes: A coupled electromechanical modeling study

Rate-dependent effects on the Ca2+ sub-system in a rat ventricular myocyte are investigated. Here, we employ a deterministic mathematical model describing various Ca2+ signalling pathways under voltage clamp (VC) conditions, to better understand the important role of calmodulin (CaM) in modulating the key control variables Ca2+/calmodulin-dependent protein kinase-II (CaMKII), calcineurin (CaN), and cyclic adenosine monophosphate (cAMP) as they affect various intracellular targets. In particular, we study the frequency dependence of the peak force generated by the myofilaments, the force-frequency response (FFR). Our cell model incorporates frequency-dependent CaM-mediated spatially heterogenous interaction of CaMKII and CaN with their principal targets (dihydropyridine (DHPR) and ryanodine (RyR) receptors and the SERCA pump). It also accounts for the rate-dependent effects of phospholamban (PLB) on the SERCA pump; the rate-dependent role of cAMP in up-regulation of the L-type Ca2+ channel (ICa;L); and the enhancement in SERCA pump activity via phosphorylation of PLB.Our model reproduces positive peak FFR observed in rat ventricular myocytes during voltage-clamp studies both in the presence/absence of cAMP mediated -adrenergic stimulation. This study provides quantitative insight into the rate-dependence of Ca2+-induced Ca2+-release (CICR) by investigating the frequency-dependence of the trigger current (ICa;L) and RyR-release. It also highlights the relative role of the sodium-calcium exchanger (NCX) and the SERCA pump at higher frequencies, as well as the rate-dependence of sarcoplasmic reticulum (SR) Ca2+ content. A rigorous Ca2+ balance imposed on our investigation of these Ca2+ signalling pathways clarifies their individual roles. Here, we present a coupled electromechanical study emphasizing the rate-dependence of isometric force developed and also investigate the temperature-dependence of FFR. Our model provides mechanistic biophysically based explanations for the rate-dependence of CICR, generating useful and testable hypotheses. Although rat ventricular myocytes exhibit a positive peak FFR in the presence/absence of beta-adrenergic stimulation, they show a characteristic increase in the positive slope in FFR due to the presence of Norepinephrine or Isoproterenol. Our study identifies cAMP-mediated stimulation, and rate-dependent CaMKII-mediated up-regulation of ICa;L as the key mechanisms underlying the aforementioned positive FFR