Ricci flow for homogeneous compact models of the universe

Using quaternions, we give a concise derivation of the Ricci tensor for homogeneous spaces with topology of the 3-dimensional sphere. We derive explicit and numerical solutions for the Ricci flow PDE and discuss their properties. In the collapse (or expansion) of these models, the interplay of the various components of the Ricci tensor are studied. We dedicate this paper to honor the work of Josh Goldberg.Comment: 18 pages, 2 figure

Non-Maxwellian Proton Velocity Distributions in Nonradiative Shocks

The Balmer line profiles of nonradiative supernova remnant shocks provide the means to measure the post-shock proton velocity distribution. While most analyses assume a Maxwellian velocity distribution, this is unlikely to be correct. In particular, neutral atoms that pass through the shock and become ionized downstream form a nonthermal distribution similar to that of pickup ions in the solar wind. We predict the H alpha line profiles from the combination of pickup protons and the ordinary shocked protons, and we consider the extent to which this distribution could affect the shock parameters derived from H alpha profiles. The Maxwellian assumption could lead to an underestimate of shock speed by up to about 15%. The isotropization of the pickup ion population generates wave energy, and we find that for the most favorable parameters this energy could significantly heat the thermal particles. Sufficiently accurate profiles could constrain the strength and direction of the magnetic field in the shocked plasma, and we discuss the distortions from a Gaussian profile to be expected in Tycho's supernova remnant.Comment: 13 pages, 6 figure

Global dynamics of the mixmaster model

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for solutions of types other than VIII and IX the singularity is velocity dominated and that the Kretschmann scalar is unbounded there, except in the explicitly known cases where the spacetime can be smoothly extended through a Cauchy horizon. For types VIII and IX it is shown that there are at most two possibilities for the evolution. When the first possibility is realized, and if the spacetime is not one of the explicitly known solutions which can be smoothly extended through a Cauchy horizon, then there are infinitely many oscillations near the singularity and the Kretschmann scalar is unbounded there. The second possibility remains mysterious and it is left open whether it ever occurs. It is also shown that any finite sequence of distinct points generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be realized approximately by a solution of the vacuum Einstein equations of Bianchi type IX.Comment: 16 page

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated

Autoantibodies against C1q as a diagnostic measure of lupus nephritis:systematic review and meta-analysis

This is a freely-available open access publication. Please cite the published version which is available via the DOI link in this record.Objectives: To evaluate the diagnostic accuracy of C1q autoantibodies in identifying lupus nephritis (LN) in patients with systemic lupus erythematosus (SLE). Data Sources and methods: Citation indexes were searched and 370 articles published from 1977 to 2013 were evaluated. The 31 selected studies included in the meta-analysis were cross-sectional in design. Among the 31 studies, 28 compared anti-C1q antibodies in 2769 SLE patients including those with (n = 1442) and without a history of LN (n = 1327). Nine studies examined anti-C1q in 517 SLE patients with active (n = 249) and inactive LN (n = 268). Hierarchical summary receiver operating characteristic (HSROC) random effects models were fitted to pool estimates of accuracy across the studies. Results: Anti-C1q antibodies discriminated between patients with and without a history of LN, with a median specificity of 73.5%. The HSROC model estimated the corresponding sensitivity to be 70.4%. A hypothetical patient with a 55% prior probability of having a history of LN as opposed to no history (the median prevalence across 28 eligible studies) would have a post-test probability of 76.4% following a positive test result (positive predictive value) or 33.0% following a negative test result (negative predictive value). For differentiating active from inactive LN the median specificity of anti-C1q antibodies was 80%, with a corresponding estimated sensitivity value 75.7% based on the HSROC model. A hypothetical patient with a 56% prior probability of active as opposed to inactive LN (the median prevalence across the 9 eligible studies) would have a post-test probability of 82.8% following a positive test result or 27.9% following a negative test result. Conclusions: Although C1q antibodies are associated with lupus nephritis the post-test probabilities are not sufficiently convincing to provide reasonable certainty of the presence or absence of history of disease/active disease.Arthritis Research UKPeninsula Collaboration for Leadership in Applied Health Research and Care (CLAHRC)National Health Service South West, funded by the National Institute for Health Research, U

Ursinus College Bulletin Vol. 10, No. 1, October 1893

A digitized copy of the October 1893 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1088/thumbnail.jp

A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is ``rotating''--i.e., is such that the stationary Killing field is not everywhere normal to the horizon--must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, $P$. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.Comment: 24 pages, no figures, v2: footnotes and references added, v3: numerous minor revision

Canonical formulation of self-gravitating spinning-object systems

Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position, linear momentum and spin variables fulfill standard Poisson bracket relations. A spatially symmetric time gauge for the tetrad field is introduced. The achieved formulation is of fully reduced form without unresolved constraints, supplementary, gauge, or coordinate conditions. The canonical field momentum is not related to the extrinsic curvature of spacelike hypersurfaces in standard ADM form. A new reduction of the tetrad degrees of freedom to the Einstein form of the metric field is suggested.Comment: 6 pages. v2: extended version; identical to the published one. v3: corrected misprints in (24) and (39); improved notation; added note regarding a further reference

Study of Flare Assessment in Systemic Lupus Erythematosus Based on Paper Patients

© 2017, The Authors. Arthritis Care & Research published by Wiley Periodicals, Inc. on behalf of American College of Rheumatology. Objective: To determine the level of agreement of disease flare severity (distinguishing severe, moderate, and mild flare and persistent disease activity) in a large paper-patient exercise involving 988 individual cases of systemic lupus erythematosus. Methods: A total of 988 individual lupus case histories were assessed by 3 individual physicians. Complete agreement about the degree of flare (or persistent disease activity) was obtained in 451 cases (46%), and these provided the reference standard for the second part of the study. This component used 3 flare activity instruments (the British Isles Lupus Assessment Group [BILAG] 2004, Safety of Estrogens in Lupus Erythematosus National Assessment [SELENA] flare index [SFI] and the revised SELENA flare index [rSFI]). The 451 patient case histories were distributed to 18 pairs of physicians, carefully randomized in a manner designed to ensure a fair case mix and equal distribution of flare according to severity. Results: The 3-physician assessment of flare matched the level of flare using the 3 indices, with 67% for BILAG 2004, 72% for SFI, and 70% for rSFI. The corresponding weighted kappa coefficients for each instrument were 0.82, 0.59, and 0.74, respectively. We undertook a detailed analysis of the discrepant cases and several factors emerged, including a tendency to score moderate flares as severe and persistent activity as flare, especially when the SFI and rSFI instruments were used. Overscoring was also driven by scoring treatment change as flare, even if there were no new or worsening clinical features. Conclusion: Given the complexity of assessing lupus flare, we were encouraged by the overall results reported. However, the problem of capturing lupus flare accurately is not completely solved