A Conformally Invariant Holographic Two-Point Function on the Berger Sphere

We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at its conformal infinity. Using basic notions from conformal geometry and the theory of boundary value problems, in particular the Dirichlet-to-Robin operator, we establish that our two-point correlation function is conformally invariant and corresponds to a boundary operator of conformal dimension one. It is plausible that the methods we use could have more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte

The Earth: Plasma Sources, Losses, and Transport Processes

This paper reviews the state of knowledge concerning the source of magnetospheric plasma at Earth. Source of plasma, its acceleration and transport throughout the system, its consequences on system dynamics, and its loss are all discussed. Both observational and modeling advances since the last time this subject was covered in detail (Hultqvist et al., Magnetospheric Plasma Sources and Losses, 1999) are addressed

Pulsar Wind Nebulae with Bow Shocks: Non-thermal Radiation and Cosmic Ray Leptons

Pulsars with high spin-down power produce relativistic winds radiating a non-negligible fraction of this power over the whole electromagnetic range from radio to gamma-rays in the pulsar wind nebulae (PWNe). The rest of the power is dissipated in the interactions of the PWNe with the ambient interstellar medium (ISM). Some of the PWNe are moving relative to the ambient ISM with supersonic speeds producing bow shocks. In this case, the ultrarelativistic particles accelerated at the termination surface of the pulsar wind may undergo reacceleration in the converging flow system formed by the plasma outflowing from the wind termination shock and the plasma inflowing from the bow shock. The presence of magnetic perturbations in the flow, produced by instabilities induced by the accelerated particles themselves, is essential for the process to work. A generic outcome of this type of reacceleration is the creation of particle distributions with very hard spectra, such as are indeed required to explain the observed spectra of synchrotron radiation with photon indices Γ≲ 1.5. The presence of this hard spectral component is specific to PWNe with bow shocks (BSPWNe). The accelerated particles, mainly electrons and positrons, may end up containing a substantial fraction of the shock ram pressure. In addition, for typical ISM and pulsar parameters, the e+ released by these systems in the Galaxy are numerous enough to contribute a substantial fraction of the positrons detected as cosmic ray (CR) particles above few tens of GeV and up to several hundred GeV. The escape of ultrarelativistic particles from a BSPWN—and hence, its appearance in the far-UV and X-ray bands—is determined by the relative directions of the interstellar magnetic field, the velocity of the astrosphere and the pulsar rotation axis. In this respect we review the observed appearance and multiwavelength spectra of three different types of BSPWNe: PSR J0437-4715, the Guitar and Lighthouse nebulae, and Vela-like objects. We argue that high resolution imaging of such objects provides unique information both on pulsar winds and on the ISM. We discuss the interpretation of imaging observations in the context of the model outlined above and estimate the BSPWN contribution to the positron flux observed at the Earth

IMPALAS: Investigation of MagnetoPause Activity using Longitudinally-Aligned Satellites—a mission concept proposed for the ESA M3 2020/2022 launch

The dayside magnetopause is the primary site of energy transfer from the solar wind into the magnetosphere, and modulates the activity observed within the magnetosphere itself. Specific plasma processes operating on the magnetopause include magnetic reconnection, generation of boundary waves, propagation of pressure-pulse induced deformations of the boundary, formation of boundary layers and generation of Alfvén waves and field-aligned current systems connecting the boundary to the inner magnetosphere and ionosphere. However, many of the details of these processes are not fully understood. For example, magnetic reconnection occurs sporadically, producing flux transfer events, but how and where these arise, and their importance to the global dynamics of the magnetospheric system remain unresolved. Many of these phenomena involve propagation across the magnetopause surface. Measurements at widely-spaced (Δ ˜ 5 RE) intervals along the direction of dayside terrestrial field lines at the magnetopause would be decisive in resolving these issues. We describe a mission carrying a fields and plasmas payload (including magnetometer, ion and electron spectrometer and energetic particle telescopes) on three identical spacecraft in synchronized orbits. These provide the needed separations, with each spacecraft skimming the dayside magnetopause and continuously sampling this boundary for many hours. The orbits are phased such that (i) all three spacecraft maintain common longitude and thus sample along the same magnetopause field line; (ii) the three spacecraft reach local midday when northern European ground-based facilities also lie near local midday, enabling simultaneous sampling of magnetopause field lines and their footprints

Indirect comparisons of competing interventions

AbstractOBJECTIVES:To survey the frequency of use of indirect comparisons in systematic reviews and evaluate the methods used in their analysis and interpretation. Also to identify alternative statistical approaches for the analysis of indirect comparisons, to assess the properties of different statistical methods used for performing indirect comparisons and to compare direct and indirect estimates of the same effects within reviews.DATA SOURCES:Electronic databases.REVIEW METHODS:The Database of Abstracts of Reviews of Effects (DARE) was searched for systematic reviews involving meta-analysis of randomised controlled trials (RCTs) that reported both direct and indirect comparisons, or indirect comparisons alone. A systematic review of MEDLINE and other databases was carried out to identify published methods for analysing indirect comparisons. Study designs were created using data from the International Stroke Trial. Random samples of patients receiving aspirin, heparin or placebo in 16 centres were used to create meta-analyses, with half of the trials comparing aspirin and placebo and half heparin and placebo. Methods for indirect comparisons were used to estimate the contrast between aspirin and heparin. The whole process was repeated 1000 times and the results were compared with direct comparisons and also theoretical results. Further detailed case studies comparing the results from both direct and indirect comparisons of the same effects were undertaken.RESULTS:Of the reviews identified through DARE, 31/327 (9.5%) included indirect comparisons. A further five reviews including indirect comparisons were identified through electronic searching. Few reviews carried out a formal analysis and some based analysis on the naive addition of data from the treatment arms of interest. Few methodological papers were identified. Some valid approaches for aggregate data that could be applied using standard software were found: the adjusted indirect comparison, meta-regression and, for binary data only, multiple logistic regression (fixed effect models only). Simulation studies showed that the naive method is liable to bias and also produces over-precise answers. Several methods provide correct answers if strong but unverifiable assumptions are fulfilled. Four times as many similarly sized trials are needed for the indirect approach to have the same power as directly randomised comparisons. Detailed case studies comparing direct and indirect comparisons of the same effect show considerable statistical discrepancies, but the direction of such discrepancy is unpredictable.CONCLUSIONS:Direct evidence from good-quality RCTs should be used wherever possible. Without this evidence, it may be necessary to look for indirect comparisons from RCTs. However, the results may be susceptible to bias. When making indirect comparisons within a systematic review, an adjusted indirect comparison method should ideally be used employing the random effects model. If both direct and indirect comparisons are possible within a review, it is recommended that these be done separately before considering whether to pool data. There is a need to evaluate methods for the analysis of indirect comparisons for continuous data and for empirical research into how different methods of indirect comparison perform in cases where there is a large treatment effect. Further study is needed into when it is appropriate to look at indirect comparisons and when to combine both direct and indirect comparisons. Research into how evidence from indirect comparisons compares to that from non-randomised studies may also be warranted. Investigations using individual patient data from a meta-analysis of several RCTs using different protocols and an evaluation of the impact of choosing different binary effect measures for the inverse variance method would also be useful