Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.Comment: 13 page

General post-Minkowskian expansion of time transfer functions

Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant $G$ (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.Comment: 10 pages. Minor modifications. Accepted in Classical and Quantum Gravit

Radioscience simulations in General Relativity and in alternative theories of gravity

In this communication, we focus on the possibility to test GR with radioscience experiments. We present a new software that in a first step simulates the Range/Doppler signals directly from the space time metric (thus in GR and in alternative theories of gravity). In a second step, a least-squares fit of the involved parameters is performed in GR. This software allows one to get the order of magnitude and the signature of the modifications induced by an alternative theory of gravity on radioscience signals. As examples, we present some simulations for the Cassini mission in Post-Einsteinian gravity and with the MOND External Field Effect.Comment: 4 pages; Proceedings of "Les Rencontres de Moriond 2011 - Gravitation session

Testing special relativity with geodetic VLBI

Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay in the barycentric reference frame. As the Earth is orbiting around the Solar system barycentre with the velocity $V$ of 30 km/s, VLBI proves to be a handy tool to detect the subtle effects of the special and general relativity theory with a magnitude of $(V/\textrm{c})^2$. The theoretical correction for the second order terms reaches up to 300~ps, and it is implemented in the geodetic VLBI group delay model. The total contribution of the second order terms splits into two effects - the variation of the Earth scale, and the deflection of the apparent position of the radio source. The Robertson-Mansouri-Sexl (RMS) generalization of the Lorenz transformation is used for many modern tests of the special relativity theory. We develop an alteration of the RMS formalism to probe the Lorenz invariance with the geodetic VLBI data. The kinematic approach implies three parameters (as a function of the moving reference frame velocity) and the standard Einstein synchronisation. A generalised relativistic model of geodetic VLBI data includes all three parameters that could be estimated. Though, since the modern laboratory Michelson-Morley and Kennedy-Thorndike experiments are more accurate than VLBI technique, the presented equations may be used to test the VLBI group delay model itself.Comment: Proceedings of the IAG 2017 Scientific Meeting, Kobe, Japa

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. The present paper gives the physical interpretation of the observed light-ray deflections and discusses the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by the Jupiter and the Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.

A universal tool for determining the time delay and the frequency shift of light: Synge's world function

In almost all of the studies devoted to the time delay and the frequency shift of light, the calculations are based on the integration of the null geodesic equations. However, the above-mentioned effects can be calculated without integrating the geodesic equations if one is able to determine the bifunction $\Omega(x_A, x_B)$ giving half the squared geodesic distance between two points $x_A$ and $x_B$ (this bifunction may be called Synge's world function). In this lecture, $\Omega(x_A, x_B)$ is determined up to the order $1/c^3$ within the framework of the PPN formalism. The case of a stationary gravitational field generated by an isolated, slowly rotating axisymmetric body is studied in detail. The calculation of the time delay and the frequency shift is carried out up to the order $1/c^4$. Explicit formulae are obtained for the contributions of the mass, of the quadrupole moment and of the internal angular momentum when the only post-Newtonian parameters different from zero are $\beta$ and $\gamma$. It is shown that the frequency shift induced by the mass quadrupole moment of the Earth at the order $1/c^3$ will amount to $10^{-16}$ in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission. Other contributions are briefly discussed.Comment: 18 pages, To appear in: "Lasers, Clocks and Drag-Free control: Exploration of Relativistic Gravity in Space", Springer Series on Astrophysics and Space Science Library, vol 349, p 15

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

An observational study of once-daily modified-release methylphenidate in ADHD: effectiveness on symptoms and impairment, and safety

ADHD affects over 5% of children worldwide. It is typically treated with stimulant medications, and methylphenidate (MPH) is the most commonly prescribed. This study investigated the effectiveness, on symptoms and impairment, and safety of Equasym XL®, a combination of 30% immediate-release and 70% modified-release MPH, in the treatment of ADHD in daily clinical practice. This open-label, observational, post-marketing surveillance study was conducted in 169 centres in Germany. Eligible patients, aged 6–17 years, were diagnosed with ADHD and about to begin treatment with Equasym XL®. Effectiveness was assessed by physicians using the clinical global impression (CGI) severity and improvement scales; teachers and parents completed questionnaires evaluating ADHD symptoms and behavioural problems (DAYAS, FBB-ADHD and SDQ-P). Assessments were carried out at baseline, after 1–3 and 6–12 weeks of treatment. Of 852 enrolled patients, 822 were evaluable; 25.30% were treatment naïve, 69.84% had previously received different MPH formulations, and 4.87% had received other medications. ADHD symptoms improved from baseline to last visit for the majority of patients for all outcome measures. According to physician ratings of core ADHD symptoms, 75.73% of patients showed improvements on the CGI-Improvement scale, 17.77% had no change, and 6.50% worsened. In teacher and parent ratings, the effectiveness of Equasym XL® was rated better than prior therapy at all measured time points across the day, particularly late morning (teachers) and early afternoon (parents). Equasym XL® was generally well tolerated; only 3.16% of patients permanently discontinued treatment due to adverse events. Equasym XL® is effective and well tolerated in daily clinical practice

Association between Proximity to a Health Center and Early Childhood Mortality in Madagascar

Objective: To evaluate the association between proximity to a health center and early childhood mortality in Madagascar, and to assess the influence of household wealth, maternal educational attainment, and maternal health on the effects of distance. Methods: From birth records of subjects in the Demographic and Health Survey, we identified 12565 singleton births from January 2004 to August 2009. After excluding 220 births that lacked global positioning system information for exposure assessment, odds ratios (ORs) and their 95% confidence intervals (CIs) for neonatal mortality and infant mortality were estimated using multilevel logistic regression models, with 12345 subjects (level 1), nested within 584 village locations (level 2), and in turn nested within 22 regions (level 3). We additionally stratified the subjects by the birth order. We estimated predicted probabilities of each outcome by a three-level model including cross-level interactions between proximity to a health center and household wealth, maternal educational attainment, and maternal anemia. Results: Compared with those who lived >1.5–3.0 km from a health center, the risks for neonatal mortality and infant mortality tended to increase among those who lived further than 5.0 km from a health center; the adjusted ORs for neonatal mortality and infant mortality for those who lived >5.0–10.0 km away from a health center were 1.36 (95% CI: 0.92–2.01) and 1.42 (95% CI: 1.06–1.90), respectively. The positive associations were more pronounced among the second or later child. The distance effects were not modified by household wealth status, maternal educational attainment, or maternal health status. Conclusions: Our study suggests that distance from a health center is a risk factor for early childhood mortality (primarily, infant mortality) in Madagascar by using a large-scale nationally representative dataset. The accessibility to health care in remote areas would be a key factor to achieve better infant health