A model problem for conformal parameterizations of the Einstein constraint equations

We investigate the possibility that the conformal and conformal thin sandwich (CTS) methods can be used to parameterize the set of solutions of the vacuum Einstein constraint equations. To this end we develop a model problem obtained by taking the quotient of certain symmetric data on conformally flat tori. Specializing the model problem to a three-parameter family of conformal data we observe a number of new phenomena for the conformal and CTS methods. Within this family, we obtain a general existence theorem so long as the mean curvature does not change sign. When the mean curvature changes sign, we find that for certain data solutions exist if and only if the transverse-traceless tensor is sufficiently small. When such solutions exist, there are generically more than one. Moreover, the theory for mean curvatures changing sign is shown to be extremely sensitive with respect to the value of a coupling constant in the Einstein constraint equations.Comment: 40 pages, 4 figure

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

A rigidity theorem for nonvacuum initial data

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no figure

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

Advances in molecular biology have led to the development of biologic therapies. This is particularly relevant in systemic lupus erythematosus (SLE), which is a multisystem autoimmune rheumatic disease (ARD) associated with potentially life-threatening complications if not adequately treated. The availability of new biologic drugs has improved the prognosis of SLE in selected cases associated with unsatisfactory response to conventional therapies. Over the last decade, there have been developments in the availability of biologic agents for SLE treatment based upon the advances in the understanding of the disease pathogenesis. Even if the evidence of biologic treatment efficacy in SLE is weaker than in other autoimmune rheumatic diseases, such as rheumatoid arthritis (RA), significant progress was made, as the first biologic treatment for use in SLE patients received approval in 2011. These new biologic therapies for SLE range from anti-CD20/CD22 (clusters of differentiation characteristic to B cells), to anti-B cell activating factors and anti-interferon alpha (IFNα). This chapter reviews the various biologic agents used in SLE, their mechanism of action and safety profile. The most common side effects to biologic treatments include infection, tuberculosis (TB) reactivation and allergic reactions. Less common side effects include development of lymphoma and anti-drug or autoimmune antibody formation. Despite their toxicity profile, biologic agents are gaining ground in clinical practice due to the limited efficacy or increased toxicity of conventional disease modifying agents (DMARD’s). Biologic therapies targeting B cells, such as rituximab, and B cell activation factors, such as belimumab, are currently used in the treatment of refractory SLE. Furthermore, aggressive treatment, including the use of biologic agents, reduces long-term complications associated with prolonged use of steroids in SLE, such as cardiovascular disease and osteoporosis. In the short term, the biologic agents are expensive when compared to traditional DMARDs; however there is evidence that their use is associated with long term benefits for patients with SLE, such as reduced hospital admission and disease complications, and improved patient outcomes. This chapter provides a summary of most biologic agents tested in SLE patients, considering their efficacy and safety profile, as well as the health implications associated with their use. We also take a brief look at newer agents currently investigated in clinical trials

The ground state and the long-time evolution in the CMC Einstein flow

Let (g,K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold M with non-positive Yamabe invariant (Y(M)). As noted by Fischer and Moncrief, the reduced volume V(k)=(-k/3)^{3}Vol_{g(k)}(M) is monotonically decreasing in the expanding direction and bounded below by V_{\inf}=(-1/6)Y(M))^{3/2}. Inspired by this fact we define the ground state of the manifold M as "the limit" of any sequence of CMC states {(g_{i},K_{i})} satisfying: i. k_{i}=-3, ii. V_{i} --> V_{inf}, iii. Q_{0}((g_{i},K_{i}))< L where Q_{0} is the Bel-Robinson energy and L is any arbitrary positive constant. We prove that (as a geometric state) the ground state is equivalent to the Thurston geometrization of M. Ground states classify naturally into three types. We provide examples for each class, including a new ground state (the Double Cusp) that we analyze in detail. Finally consider a long time and cosmologically normalized flow (\g,\K)(s)=((-k/3)^{2}g,(-k/3))K) where s=-ln(-k) is in [a,\infty). We prove that if E_{1}=E_{1}((\g,\K))< L (where E_{1}=Q_{0}+Q_{1}, is the sum of the zero and first order Bel-Robinson energies) the flow (\g,\K)(s) persistently geometrizes the three-manifold M and the geometrization is the ground state if V --> V_{inf}.Comment: 40 pages. This article is an improved version of the second part of the First Version of arXiv:0705.307

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

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit

Gluing Initial Data Sets for General Relativity

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Secondly, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.Comment: Final published version - PRL, 4 page

Direct Oral Anticoagulants for Thromboprophylaxis in Patients with Antiphospholipid Syndrome

The current mainstay of the treatment and secondary thromboprophylaxis of thrombotic antiphospholipid syndrome (APS) is anticoagulation with warfarin or other vitamin K antagonists (VKAs). In addition to their well-known limitations, VKAs are often problematic in APS patients because of the variable sensitivity of thromboplastins to lupus anticoagulant. As a result, the international normalized ratio may not accurately reflect the intensity of anticoagulation. Direct oral anticoagulants (DOACs) are established as therapeutic alternatives to VKAs for a wide range of indications, including the treatment and secondary prevention of venous thromboembolism. Definition of the role of DOACs in the treatment of thrombotic APS is emerging with the results of recent and ongoing clinical studies. This review focuses on the current situation with regard to DOACs for secondary thromboprophylaxis in APS and issues pertinent to DOAC use in APS patients, as well as potential future directions

Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.Comment: 37 pages; 2 figure