Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.Comment: 15 page

Biologic therapies for systemic lupus erythematosus: where are we now?

PURPOSE OF REVIEW: Conventional approaches using hydroxychloroquine, corticosteroids and immunosuppressives have improved the prognosis for systemic lupus erythematosus (SLE) patients. Unfortunately, they have reached the limits of what they can achieve and patients still die prematurely and/or find their quality of life greatly impaired. Here, we discuss the problems of assessing activity in SLE, optimizing clinical trial design and more recent biologic approaches. RECENT FINDINGS: The success of B-cell depletion using Rituximab in open clinical studies, the approval of Belimumab (blocks the B-cell activating factor BAFF) and improvements in clinical trial design, gives cause for hope. Approaches including the use of fully humanized anti-CD20 and CD19 monoclonals, blocking interferons, inhibiting Bruton's tyrosine kinase (BTK), blocking the CD40 ligand (CD40L), utilizing an analogue of the FcɣRIIB and an IL12-23 blocker and targeting the JAK-STAT pathway have met end points in phase II and III trials. SUMMARY: For 20 years, we hoped that the successes of the biologic therapies in rheumatoid arthritis and psoriatic arthritis would be replicated in SLE but we have been generally disappointed. However, the encouraging recent results with monoclonals that block interferon and fully humanized anti-CD20 in particular, offer the prospect of a real revolution in the treatment of SLE

Resonant Interactions Between Protons and Oblique Alfv\'en/Ion-Cyclotron Waves

Resonant interactions between ions and Alfv\'en/ion-cyclotron (A/IC) waves may play an important role in the heating and acceleration of the fast solar wind. Although such interactions have been studied extensively for "parallel" waves, whose wave vectors ${\bf k}$ are aligned with the background magnetic field ${\bf B}_0$, much less is known about interactions between ions and oblique A/IC waves, for which the angle $\theta$ between ${\bf k}$ and ${\bf B}_0$ is nonzero. In this paper, we present new numerical results on resonant cyclotron interactions between protons and oblique A/IC waves in collisionless low-beta plasmas such as the solar corona. We find that if some mechanism generates oblique high-frequency A/IC waves, then these waves initially modify the proton distribution function in such a way that it becomes unstable to parallel waves. Parallel waves are then amplified to the point that they dominate the wave energy at the large parallel wave numbers at which the waves resonate with the particles. Pitch-angle scattering by these waves then causes the plasma to evolve towards a state in which the proton distribution is constant along a particular set of nested "scattering surfaces" in velocity space, whose shapes have been calculated previously. As the distribution function approaches this state, the imaginary part of the frequency of parallel A/IC waves drops continuously towards zero, but oblique waves continue to undergo cyclotron damping while simultaneously causing protons to diffuse across these kinetic shells to higher energies. We conclude that oblique A/IC waves can be more effective at heating protons than parallel A/IC waves, because for oblique waves the plasma does not relax towards a state in which proton damping of oblique A/IC waves ceases

Ricci flows, wormholes and critical phenomena

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that observed in gravitational collapse. Similar results are obtained for initial data that describe space bubbles attached to asymptotically flat regions. Our numerical methods are applicable to "matter-coupled" Ricci flows derived from conformal invariance in string theory.Comment: 8 pages, 5 figures. References added and minor changes to match version accepted by CQG as a fast track communicatio

Computer analyses suggest interactions of non-muscle filamin with lipid membranes

AbstractIt is concluded from structure predictions of the primary amino acid sequence by computer analyses that two segments of non-muscle filamin could facilitate lipid membrane attachment or anchoring. Residues 49–71 of the amino-terminal may attach to phospholipid membranes, and residues 131–155 may anchor in the hydrophobic region of lipid membranes

Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes

We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish an existence and uniqueness theory for this problem with smooth data and smooth coefficients (and with even lower regularity). We apply this theory in order to show the existence of smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein equations, which exhibit AVTD (asymptotically velocity term dominated) behavior in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page

Low-Energy Dynamics of String Solitons

The dynamics of a class of fivebrane string solitons is considered in the moduli space approximation. The metric on moduli space is found to be flat. This implies that at low energies the solitons do not interact, and their scattering is trivial. The range of validity of the approximation is also briefly discussed.Comment: 8 pages, Minor typos correcte