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

B-cell depletion in SLE: clinical and trial experience with rituximab and ocrelizumab and implications for study design.

B cells are believed to be central to the disease process in systemic lupus erythematosus (SLE), making them a target for new therapeutic intervention. In recent years there have been many publications regarding the experience in SLE of B-cell depletion utilising rituximab, an anti-CD20 mAb that temporarily depletes B cells,reporting promising results in uncontrolled open studies and in routine clinical use. However, the two large randomised controlled trials in extra-renal lupus (EXPLORER study) and lupus nephritis (LUNAR study) failed to achieve their primary endpoints. Based on the clinical experience with rituximab this failure was somewhat unexpected and raised a number of questions and concerns, not only into the true level of benefit of B-cell depletion in a broad population but also how to test the true level of effectiveness of an investigational agent as we seek to improve the design of therapeutic trials in SLE. A better understanding of what went wrong in these trials is essential to elucidate the underlying reasons for the disparate observations noted in open studies and controlled trials. In this review, we focus on various factors that may affect the ability to accurately and confidently establish the level of treatment effect of the investigational agent, in this case rituximab, in the tw studies and explore hurdles faced in the randomised controlled trials investigating the efficacy of ocrelizumab, the humanised anti-CD20 mAb, in SLE. Further, based on the lessons learned from the clinical trials, we make suggestions that could be implemented in future clinical trial design to overcome the hurdles faced

Kidney disease in primary anti-phospholipid antibody syndrome

APS is an autoimmune disease defined by the presence of arterial or venous thrombotic events and/or pregnancy morbidity in patients who test positive for aPL. APS can be isolated (primary APS) or associated with other autoimmune diseases. The kidney is a major target organ in APS, and renal thrombosis can occur at any level within the vasculature of the kidney (renal arteries, intrarenal vasculature and renal veins). Histological findings vary widely, including ischaemic glomeruli and thrombotic lesions without glomerular or arterial immune deposits on immunofluorescence. Renal involvement in patients with definite APS is treated with long-term anticoagulants as warfarin, but new treatments are being tried. The aim of this article is to review the links between primary APS and kidney disease

Clinical trials in systemic lupus erythematosus: the dilemma—Why have phase III trials failed to confirm the promising results of phase II trials?

Systemic lupus erythematosus (SLE) is an autoimmune rheumatic disease of unknown aetiology, characterised by the production of auto-antibodies and formation of immune complexes against self-antigens and complement activation. This inflammatory response can lead to tissue infiltration and eventually, to organ damage.Patients with SLE invariably have periods of relapse and remission. Flares can occur even when the patient is on seemingly adequate treatment, which suggests that more effective therapies are necessary for the management of SLE. Thus, trials with many drugs against different targets, such as CD22, IL-12 and IL-23 or tyrosine kinases, have been carried out in recent years.A frustrating feature of some of the biologic drugs used to treat SLE has been the reporting of successful phase II trials followed by failures of the phase III trials.In this review, we will focus on phase II and III trials carried out with epratuzumab (anti CD22), baricitinib (Janus kinases inhibitor), rigerimod (P140 peptide) and ustekinumab (IL-12 and IL-23 inhibitor) and consider the reasons for their ultimate failure to 'make the grade'. Likewise, we will try to explain the possible reasons that can influence why good results may be obtained in phase II trials and lead to undue optimism

THBS1 (thrombospondin-1)

Thrombospondins are encoded in vertebrates by a family of 5 THBS genes. THBS1 is infrequently mutated in most cancers, but its expression is positively regulated by several tumor suppressor genes and negatively regulated by activated oncogenes and promoter hypermethylation. Consequently, loss of thrombospondin-1 expression is frequently lost during oncogenesis and is correlated with a poor prognosis for some cancers. Thrombospondin-1 is a secreted protein that acts in the tumor microenvironment to inhibit angiogenesis, regulate antitumor immunity, stimulate tumor cell migration, and regulate the activities of extracellular proteases and growth factors. Differential effects of thrombospondin-1 on the sensitivity of normal versus malignant cells to ischemic and genotoxic stress also regulate the responses to tumors to therapeutic radiation and chemotherapy

The use of rituximab in newly diagnosed patients with systemic lupus erythematosus: long-term steroid saving capacity and clinical effectiveness

Background: Previous reports indicate that treating patients with lupus (SLE) at or close to the time of diagnosis successfully without using any, or minimal, corticosteroids by using B-cell depletion (BCD) is possible in the short-term. It is not however known whether using BCD is as effective or reduces corticosteroid use in the long-term. We report the long-term (up to 7 years) use of BCD with respect to its steroid-saving capacity and clinical effectiveness in newly diagnosed SLE. Methods: Sixteen female patients with SLE were treated at, or shortly after diagnosis, with BCD therapy (BCDT) minimising the routine use of oral steroids. Post-treatment, most patients were given hydroxychloroquine (n=14) and azathioprine (n=10). The British Isles Lupus Assessment Group (BILAG) disease activity index was used for clinical assessment. Serum antidouble-stranded DNA (dsDNA) antibodies, complement (C3), erythrocyte sedimentation rate (ESR), circulating B lymphocytes (CD19+) and total inmmunoglobulins were tested every 2-6 months (average of 4.5 years) (SD 2) post-treatment. Disease activity and steroid requirement were compared with three patients with SLE treated conventionally, each matched for ethnicity, sex, age, clinical features, disease duration at diagnosis and follow-up period. Results: All patients given rituximab achieved BCD. The mean number of flares during follow-up (new BILAG A or B) was 2.63 (SD 3) in the BCDT group and 4 (SD 3.6) in the controls (NS, p=0.14). Post-BCDT, mean anti-dsDNA antibody level fell from 1114 U/mL (SD 1699.3) to 194 (SD 346.7) at 18 months (p=0.043), mean serum ESR fell by >70% at 6 months maintained during follow-up and serum C3 level normalised in 8 patients. The mean cumulative prednisolone dose at 60 months for the patients who underwent BCDT (n=11) was 4745.67 mg (SD 6090 mg) vs 12 553.92 mg (SD 12 672 mg) for the controls (p=0.01). Conclusions: Early treatment of patients with SLE with BCDT is safe, effective and enables a reduction in steroid use

Asymptotic behavior of unstable perturbations of the Fubini-Study metric in Ricci flow

Kr\"oncke has shown that the Fubini-Study metric is an unstable generalized stationary solution of Ricci flow [Kr\"o20]. In this paper, we carry out numerical simulations which indicate that Ricci flow solutions originating at unstable perturbations of the Fubini-Study metric develop local singularities modeled by the blowdown soliton discovered in [FIK03].Comment: 14 pages, 3 figures. Comments are welcome

On the constraint equations in Einstein-aether theories and the weak gravitational field limit

We discuss the set of constraints for Einstein-aether theories, comparing the flat background case with what is expected when the gravitational fields are dynamic. We note potential pathologies occurring in the weak gravitational field limit for some of the Einstein-aether theories