Translations and dynamics

We analyze the role played by local translational symmetry in the context of gauge theories of fundamental interactions. Translational connections and fields are introduced, with special attention being paid to their universal coupling to other variables, as well as to their contributions to field equations and to conserved quantities.Comment: 22 Revtex pages, no figures. Published version with minor correction

Profiles of inflated surfaces

We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which we describe explicitly as the solutions of a certain differential equation.Comment: 13 pages, 2 figure

A gauge theoretical view of the charge concept in Einstein gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\hbar/l^2$, the mass parameter of a particle dimension $\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi-electric monopole charge of the time translation whereas the NUT parameter is a quasi-magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio

Nonsense mutations in alpha-II spectrin in three families with juvenile onset hereditary motor neuropathy

Distal hereditary motor neuropathies are a rare subgroup of inherited peripheral neuropathies hallmarked by a length-dependent axonal degeneration of lower motor neurons without significant involvement of sensory neurons. We identified patients with heterozygous nonsense mutations in the alpha II-spectrin gene, SPTAN1, in three separate dominant hereditary motor neuropathy families via next-generation sequencing. Variable penetrance was noted for these mutations in two of three families, and phenotype severity differs greatly between patients. The mutant mRNA containing nonsense mutations is broken down by nonsense-mediated decay and leads to reduced protein levels in patient cells. Previously, dominant-negative alpha II-spectrin gene mutations were described as causal in a spectrum of epilepsy phenotypes

Geodesic Deviation in Regge Calculus

Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of general relativity on two different levels. We show that the continuum and simplicial descriptions coincide when the cumulative effect of the Regge contributions over an infinitesimal element of area is considered. This comparison provides a quantitative relation between the curvature of the continuous description and the deficit angles of Regge calculus. The results presented might also be of help in developing generic ways of including matter terms in the Regge equations.Comment: 9 pages. Latex 2e with 5 EPS figures. Submitted to CQ

Long-term efficacy and safety of eculizumab in Japanese patients with generalized myasthenia gravis : a subgroup analysis of the REGAIN open-label extension study

The terminal complement inhibitor eculizumab was shown to improve myasthenia gravis-related symptoms in the 26-week, phase 3, randomized, double-blind, placebo-controlled REGAIN study (NCT01997229). In this 52-week sub-analysis of the open-label extension of REGAIN (NCT02301624), eculizumab's efficacy and safety were assessed in 11 Japanese and 88 Caucasian patients with anti-acetylcholine receptor antibody-positive refractory generalized myasthenia gravis. For patients who had received placebo during REGAIN, treatment with open-label eculizumab resulted in generally similar outcomes in the Japanese and Caucasian populations. Rapid improvements were maintained for 52 weeks, assessed by change in score from open-label extension baseline to week 52 (mean [standard error]) using the following scales (in Japanese and Caucasian patients, respectively): Myasthenia Gravis Activities of Daily Living (-2.4 [1.34] and - 3.3 [0.651); Quantitative Myasthenia Gravis (-2.9 [1.98] and - 4.3 [0.79]); Myasthenia Gravis Composite (-4.5 [2.63] and - 4.9 [1.19]); and Myasthenia Gravis Quality of Life 15-item questionnaire (-8.6 [5.68) and - 6.5 [1.93]). Overall, the safety of eculizumab was consistent with its known safety profile. In this interim sub-analysis, the efficacy and safety of eculizumab in Japanese and Caucasian patients were generally similar, and consistent with the overall REGAIN population

A Categorical Equivalence between Generalized Holonomy Maps on a Connected Manifold and Principal Connections on Bundles over that Manifold

A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys. 30(9), (1991)], establishes that given a "generalized" holonomy map from the space of piece-wise smooth, closed curves based at some point of a manifold to a Lie group, there exists a principal bundle with that group as structure group and a principal connection on that bundle such that the holonomy map corresponds to the holonomies of that connection. Barrett also provided one sense in which this "recovery theorem" yields a unique bundle, up to isomorphism. Here we show that something stronger is true: with an appropriate definition of isomorphism between generalized holonomy maps, there is an equivalence of categories between the category whose objects are generalized holonomy maps on a smooth, connected manifold and whose arrows are holonomy isomorphisms, and the category whose objects are principal connections on principal bundles over a smooth, connected manifold. This result clarifies, and somewhat improves upon, the sense of "unique recovery" in Barrett's theorems; it also makes precise a sense in which there is no loss of structure involved in moving from a principal bundle formulation of Yang-Mills theory to a holonomy, or "loop", formulation.Comment: 20 page

Gravitational Waves: Just Plane Symmetry

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.Comment: 10 pages, TeX, uses IOP style file

Consistent improvement with eculizumab across muscle groups in myasthenia gravis

Objective: To assess whether eculizumab, a terminal complement inhibitor, improves patient- and physician-reported outcomes (evaluated using the myasthenia gravis activities of daily living profile and the quantitative myasthenia gravis scale, respectively) in patients with refractory anti-acetylcholine receptor antibody-positive generalized myasthenia gravis across four domains, representing ocular, bulbar, respiratory, and limb/gross motor muscle groups. Methods: Patients with refractory anti-acetylcholine receptor antibody-positive generalized myasthenia gravis were randomized 1:1 to receive either placebo or eculizumab during the REGAIN study (NCT01997229). Patients who completed REGAIN were eligible to continue into the open-label extension trial (NCT02301624) for up to 4 years. The four domain scores of each of the myasthenia gravis activities of daily living profile and the quantitative myasthenia gravis scale recorded throughout REGAIN and through 130 weeks of the open-label extension were analyzed. Results: Of the 125 patients who participated in REGAIN, 117 enrolled in the open-label extension; 61 had received placebo and 56 had received eculizumab during REGAIN. Patients experienced rapid improvements in total scores and all four domain scores of both the myasthenia gravis activities of daily living profile and the quantitative myasthenia gravis scale with eculizumab treatment. These improvements were sustained through 130 weeks of the open-label extension. Interpretation: Eculizumab treatment elicits rapid and sustained improvements in muscle strength across ocular, bulbar, respiratory, and limb/gross motor muscle groups and in associated daily activities in patients with refractory anti-acetylcholine receptor antibody-positive generalized myasthenia gravis

Localization via Automorphisms of the CARs. Local gauge invariance

The classical matter fields are sections of a vector bundle E with base manifold M. The space L^2(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of C_b^\infty(M) on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action defines an automorphism group on the algebra A, of the canonical anticommutation relations on L^2(E), with which we can perform the analogous localization. That is, the net structure of the CAR, A, w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction maps. As a corollary, we prove a well-known "folk theorem," that the algebra A contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E.Comment: 15 page