Symmetry reduction, integrability and reconstruction in k-symplectic field theory

We investigate the reduction process of a k-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial differential equations, the so-called Lagrange-Poincare field equations. We discuss two issues about reconstructing a solution from a given solution of the reduced equations. The first one is an interpretation of the integrability conditions, in terms of the curvatures of some connections. The second includes the introduction of the concept of a k-connection to provide a reconstruction method. We show that an invariant Lagrangian, under suitable regularity conditions, defines a `mechanical' k-connection.Comment: 37 page

Effectiveness of delayed-release dimethyl fumarate on patient-reported outcomes and clinical measures in patients with relapsing-remitting multiple sclerosis in a real-world clinical setting: PROTEC.

Ensaio clínico PROTEC, Protocolo nº 109MS408Abstract BACKGROUND: Patient-reported outcomes (PRO) and clinical outcomes give a broad assessment of relapsing-remitting multiple sclerosis (RRMS) disease. OBJECTIVE: The aim is to evaluate the effectiveness of delayed-release dimethyl fumarate (DMF) on disease activity and PROs in patients with RRMS in the clinic. METHODS: PROTEC, a phase 4, open-label, 12-month observational study, assessed annualized relapse rate (ARR), proportion of patients relapsed, and changes in PROs. Newly diagnosed and early MS (≤3.5 EDSS and ≤1 relapse in the prior year) patient subgroups were evaluated. RESULTS: Unadjusted ARR at 12 months post-DMF versus 12 months before DMF initiation was 75% lower (0.161 vs. 0.643, p < 0.0001) overall (n = 1105) and 84%, 77%, and 71% lower in newly diagnosed, ≤3.5 EDSS, and ≤1 relapse subgroups, respectively. Overall, 88% of patients were relapse-free 12 months after DMF initiation (84%, newly diagnosed; 88%, ≤3.5 EDSS; 88%, ≤1 relapse). PRO measures for fatigue, treatment satisfaction, daily living, and work improved significantly over 12 months of DMF versus baseline. CONCLUSION: At 12 months after versus 12 months before DMF initiation, ARR was significantly lower, the majority of patients were relapse-free, and multiple PRO measures showed improvement (overall and for subgroups), suggesting that DMF is effective based on clinical outcomes and from a patient perspective.Clinical trial: A Study Evaluating the Effectiveness of Tecfidera (Dimethyl Fumarate) on Multiple Sclerosis (MS) Disease Activity and Patient-Reported Outcomes (PROTEC), NCT01930708,info:eu-repo/semantics/publishedVersio

On attributes of a Rotating Neutron star with a Hyperon core

We study the effect of rotation on global properties of neutron star with a hyperon core in an effective chiral model with varying nucleon effective mass within a mean field approach. The resulting gross properties of the rotating compact star sequences are then compared and analyzed with other theoretical predictions and observations from neutron stars. The maximum mass of the compact star predicted by the model lies in the range $(1.4-2.4) ~M_{\odot}$ at Kepler frequency $\Omega_K$, which is consistant with recent observation of high mass stars thereby reflecting the sensitivity of the underlying nucleon effective mass in the dense matter EoS. We also discuss the implications of the experimental constraints from the flow data from heavy-ion collisions on the global properties of the rotating neutron stars.Comment: 11 Pages, 10 Figures and 2 Table

Relativistic precession around rotating neutron stars: Effects due to frame-dragging and stellar oblateness

General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole effect and relativistic corrections. The first post-Newtonian correction to the Newtonian quadrupole precession is derived in the limit of slow rotation. We show that the post-Newtonian precession formula is a good approximation to the exact precession close to the neutron star in the slow rotation limit (up to \sim 400 Hz in the present context). The results are applied to recent RXTE observations of neutron star low-mass X-ray binaries, which display kHz quasi-periodic oscillations and, within the framework of beat frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of matter in the accretion disk around it. For a wide range of realistic equations of state, we find that the predicted precession frequency of this ring is close to one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations seen in several Atoll sources.Comment: 35 pages including 10 figures and 6 tables. To appear in the Astrophysical Journa

Differential Rotation in Neutron Stars: Magnetic Braking and Viscous Damping

Diffferentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars, according to general relativity. The remnant of a binary neutron star merger may give rise to such a ``hypermassive'' object. While such a star may be dynamically stable against gravitational collapse and bar formation, the radial stabilization due to differential rotation is likely to be temporary. Magnetic braking and viscosity combine to drive the star to uniform rotation, even if the seed magnetic field and the viscosity are small. This process inevitably leads to delayed collapse, which will be accompanied by a delayed gravitational wave burst and, possibly, a gamma-ray burst. We provide a simple, Newtonian, MHD calculation of the braking of differential rotation by magnetic fields and viscosity. The star is idealized as a differentially rotating, infinite cylinder consisting of a homogeneous, incompressible conducting gas. We solve analytically the simplest case in which the gas has no viscosity and the star resides in an exterior vacuum. We treat numerically cases in which the gas has internal viscosity and the star is embedded in an exterior, low-density, conducting medium. Our evolution calculations are presented to stimulate more realistic MHD simulations in full 3+1 general relativity. They serve to identify some of the key physical and numerical parameters, scaling behavior and competing timescales that characterize this important process.Comment: 11 pages. To appear in ApJ (November 20, 2000

Initial State: Theory Status

I present a brief discussion of the different approaches to the study initial state effects in heavy ion collisions in view of the recent results from Pb+Pb and p+p collisions at the LHC.Comment: 8 pages, 6 figures. Contribution to the proceedings of the XXII International Conference on Ultrarelativistic Nucleus-Nucleus Collisions, QM2011. Annecy, France, 22-28 May 201

Redox Regulation, Rather than Stress-Induced Phosphorylation, of a Hog1 Mitogen-Activated Protein Kinase Modulates Its Nitrosative-Stress-Specific Outputs

Data availability. The RNA sequencing dataset is available at EBI (www.ebi.ac.uk/arrayexpress/) under accession number E-MTAB-5990. Other data that support the findings of this study are available from the corresponding author upon reasonable request. ACKNOWLEDGMENTS We thank Debbie Smith for constructing the strains JC41 and JC310, Arnab Pradhan for help with DHE control experiments, and our colleagues in the Aberdeen Fungal Group and Newcastle Yeast Group for insightful discussions. We are also grateful to Mike Gustin for his advice. We are grateful to the Centre for Genome Enabled Biology and Medicine, Aberdeen Proteomics, the Iain Fraser Cytometry Centre, the Microscopy and Histology Facility, and the qPCR facility at the University of Aberdeen for their help, advice, and support. This work was funded by the UK Biotechnology and Biological Research Council (http://www.bbsrc.ac.uk) (grants BB/K017365/1 and BB/F00513X/1 to A.J.P.B. and grant BB/K016393/1 to J.Q.). This work was also supported by the European Research Council (http://erc.europa.eu/) (STRIFE advanced grant C-2009-AdG-249793 to A.J.P.B.), the UK Medical Research Council (http://www.mrc.ac.uk) (grant MR/M026663/1 to A.J.P.B. and grant MR/M000923/1 to P.S.S.), the Wellcome Trust (https://wellcome.ac.uk) (grant 097377 to A.J.P.B. and J.Q.), the MRC Centre for Medical Mycology and the University of Aberdeen (grant MR/M026663/1 to A.J.P.B.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Gravitational waves from pulsations of neutron stars described by realistic Equations of State

In this work we discuss the time-evolution of nonspherical perturbations of a nonrotating neutron star described by a realistic Equation of State (EOS). We analyze 10 different EOS for a large sample of neutron star models. Various kind of generic initial data are evolved and the corresponding gravitational wave signals are computed. We focus on the dynamical excitation of fluid and spacetime modes and extract the corresponding frequencies. We employ a constrained numerical algorithm based on standard finite differencing schemes which permits stable and long term evolutions. Our code provides accurate waveforms and allows to capture, via Fourier analysis of the energy spectra, the frequencies of the fluid modes with an accuracy comparable to that of frequency domain calculations. The results we present here are useful for provindig comparisons with simulations of nonlinear oscillations of (rotating) neutron star models as well as testbeds for 3D nonlinear codes.Comment: 17 pages, 9 figures. Small changes. Version published in Phys. Rev.

A comment on "The Cauchy problem of f(R)- gravity", Class. Quantum Grav., 24, 5667 (2007), arXiv:0709.4414

A critical comment on [N. Lanahan--Tremblay and V. Faraoni, 2007, {\it Class. Quantum Grav.}, {\bf 24}, 5667, arXiv:0709.4414] is given discussing the well-formulation of the Chauchy problem for $f(R)$-gravity in metric-affine theories.Comment: 3 page