Canonical Melnikov theory for diffeomorphisms

We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or Melnikov displacement can be written in a canonical way. This function is defined to be a section of the normal bundle of the saddle connection. We show how our definition reproduces the classical methods of Poincar\'{e} and Melnikov and specializes to methods previously used for exact symplectic and volume-preserving maps. We use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the Melnikov displacement.Comment: laTeX, 31 pages, 3 figure

The Wow Factor? A Comparative Study of the Development of Student Music Teachers' Talents in Scotland and Australia

For some time there has been debate about differing perspectives on musical gift and musical intelligence. One view is that musical gift is innate: that it is present in certain individuals from birth and that the task of the teacher is to develop the potential which is there. A second view is that musical gift is a complex concept which includes responses from individuals to different environments and communities (Howe and Sloboda, 1997). This then raises the possibility that musical excellence can be taught. We have already explored this idea with practising musicians (Stollery and McPhee, 2002). Our research has now expanded to include music teachers in formation, and, in this paper, we look at the influences in their musical development which have either 'crystallised' or 'paralysed' the musical talent which they possess. Our research has a comparative dimension, being carried out in Scotland and in Australia. We conclude that there are several key influences in the musical development of the individual, including home and community support, school opportunities and teaching styles and that there may be education and culture-specific elements to these influences

Use of social networks as a CSR communication tool

The aim of this paper is to analyse the use of online social networks as a tool for Corporate Social Responsibility (CSR) communication and management. To this end, an analysis was performed of the messages posted by the 20 Spanish companies with the highest market capitalisation and the responses that they received on two of the most popular online social networks, Facebook and Twitter. The results of the analysis of these data show that the tendency has been to use social networks for the one-way communication of aspects of CSR related with the organisation. Therefore, it is necessary to change the way companies communicate their CSR issues by shifting to a two-way communication approach, as has been the case in other kinds of enterprise relations with their stakeholders.The authors received no direct funding for this research

The macroeconomics of a financial Dutch disease

We describe the medium-run macroeconomic effects and long-run development consequences of a financial Dutch disease that may take place in a small developing country with abundant natural resources. The first move is in financial markets. An initial surge in foreign direct investment targeting natural resources sets in motion a perverse cycle between exchange rate appreciation and mounting short- and medium-term capital flows. Such a spiral easily leads to exchange rate volatility, capital reversals, and sharp macroeconomic instability. In the long run, macroeconomic instability and overdependence on natural resource exports dampen the development of nontraditional tradable goods sectors and curtail labor productivity dynamics. We advise the introduction of constraints to short- and medium-term capital flows to tame exchange rate/capital flows boom-and-bust cycles. We support the implementation of a developmentalist monetary policy targeting competitive nominal and real exchange rates in order to encourage product and export diversification

Gaia Data Release 2 Mapping the Milky Way disc kinematics

Context. The second Gaia data release (Gaia DR2) contains high-precision positions, parallaxes, and proper motions for 1.3 billion sources as well as line-of-sight velocities for 7.2 million stars brighter than G(RVS) = 12 mag. Both samples provide a full sky coverage. Aims. To illustrate the potential of Gaia DR2, we provide a first look at the kinematics of the Milky Way disc, within a radius of several kiloparsecs around the Sun. Methods. We benefit for the first time from a sample of 6.4 million F-G-K stars with full 6D phase-space coordinates, precise parallaxes (sigma((omega) over bar)/(omega) over bar Results. Gaia DR2 allows us to draw 3D maps of the Galactocentric median velocities and velocity dispersions with unprecedented accuracy, precision, and spatial resolution. The maps show the complexity and richness of the velocity field of the galactic disc. We observe streaming motions in all the components of the velocities as well as patterns in the velocity dispersions. For example, we confirm the previously reported negative and positive galactocentric radial velocity gradients in the inner and outer disc, respectively. Here, we see them as part of a non-axisymmetric kinematic oscillation, and we map its azimuthal and vertical behaviour. We also witness a new global arrangement of stars in the velocity plane of the solar neighbourhood and in distant regions in which stars are organised in thin substructures with the shape of circular arches that are oriented approximately along the horizontal direction in the U - V plane. Moreover, in distant regions, we see variations in the velocity substructures more clearly than ever before, in particular, variations in the velocity of the Hercules stream. Conclusions. Gaia DR2 provides the largest existing full 6D phase-space coordinates catalogue. It also vastly increases the number of available distances and transverse velocities with respect to Gaia DR1. Gaia DR2 offers a great wealth of information on the Milky Way and reveals clear non-axisymmetric kinematic signatures within the Galactic disc, for instance. It is now up to the astronomical community to explore its full potential.Peer reviewe

Elective cancer surgery in COVID-19-free surgical pathways during the SARS-CoV-2 pandemic: An international, multicenter, comparative cohort study

PURPOSE As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19–free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19–free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19–free surgical pathways. Patients who underwent surgery within COVID-19–free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19–free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score–matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19–free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION Within available resources, dedicated COVID-19–free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Elective Cancer Surgery in COVID-19-Free Surgical Pathways During the SARS-CoV-2 Pandemic: An International, Multicenter, Comparative Cohort Study.

PURPOSE: As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19-free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS: This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19-free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS: Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19-free surgical pathways. Patients who underwent surgery within COVID-19-free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19-free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score-matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19-free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION: Within available resources, dedicated COVID-19-free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Gaia Data Release 2. Kinematics of globular clusters and dwarf galaxies around the Milky Way

AIMS: The goal of this paper is to demonstrate the outstanding quality of the second data release of the Gaia mission and its power for constraining many different aspects of the dynamics of the satellites of the Milky Way. We focus here on determining the proper motions of 75 Galactic globular clusters, nine dwarf spheroidal galaxies, one ultra-faint system, and the Large and Small Magellanic Clouds. METHODS: Using data extracted from the Gaia archive, we derived the proper motions and parallaxes for these systems, as well as their uncertainties. We demonstrate that the errors, statistical and systematic, are relatively well understood. We integrated the orbits of these objects in three different Galactic potentials, and characterised their properties. We present the derived proper motions, space velocities, and characteristic orbital parameters in various tables to facilitate their use by the astronomical community. RESULTS: Our limited and straightforward analyses have allowed us for example to (i) determine absolute and very precise proper motions for globular clusters; (ii) detect clear rotation signatures in the proper motions of at least five globular clusters; (iii) show that the satellites of the Milky Way are all on high-inclination orbits, but that they do not share a single plane of motion; (iv) derive a lower limit for the mass of the Milky Way of 9.1{_₂.₆⁺⁶·²} x 10¹¹ M⊙ based on the assumption that the Leo I dwarf spheroidal is bound; (v) derive a rotation curve for the Large Magellanic Cloud based solely on proper motions that is competitive with line-of-sight velocity curves, now using many orders of magnitude more sources; and (vi) unveil the dynamical effect of the bar on the motions of stars in the Large Magellanic Cloud. CONCLUSIONS: All these results highlight the incredible power of the Gaia astrometric mission, and in particular of its second data release

Gaia Data Release 2 Variable stars in the colour-absolute magnitude diagram

Context. The ESA Gaia mission provides a unique time-domain survey for more than 1.6 billion sources with G ≲ 21 mag. Aims. We showcase stellar variability in the Galactic colour-absolute magnitude diagram (CaMD). We focus on pulsating, eruptive, and cataclysmic variables, as well as on stars that exhibit variability that is due to rotation and eclipses. Methods. We describe the locations of variable star classes, variable object fractions, and typical variability amplitudes throughout the CaMD and show how variability-related changes in colour and brightness induce “motions”. To do this, we use 22 months of calibrated photometric, spectro-photometric, and astrometric Gaia data of stars with a significant parallax. To ensure that a large variety of variable star classes populate the CaMD, we crossmatched Gaia sources with known variable stars. We also used the statistics and variability detection modules of the Gaia variability pipeline. Corrections for interstellar extinction are not implemented in this article. Results. Gaia enables the first investigation of Galactic variable star populations in the CaMD on a similar, if not larger, scale as was previously done in the Magellanic Clouds. Although the observed colours are not corrected for reddening, distinct regions are visible in which variable stars occur. We determine variable star fractions to within the current detection thresholds of Gaia. Finally, we report the most complete description of variability-induced motion within the CaMD to date. Conclusions. Gaia enables novel insights into variability phenomena for an unprecedented number of stars, which will benefit the understanding of stellar astrophysics. The CaMD of Galactic variable stars provides crucial information on physical origins of variability in a way that has previously only been accessible for Galactic star clusters or external galaxies. Future Gaia data releases will enable significant improvements over this preview by providing longer time series, more accurate astrometry, and additional data types (time series BP and RP spectra, RVS spectra, and radial velocities), all for much larger samples of stars

Gaia Data Release 2 Observations of solar system objects

CONTEXT: The Gaia spacecraft of the European Space Agency (ESA) has been securing observations of solar system objects (SSOs) since the beginning of its operations. Data Release 2 (DR2) contains the observations of a selected sample of 14,099 SSOs. These asteroids have been already identified and have been numbered by the Minor Planet Center repository. Positions are provided for each Gaia observation at CCD level. As additional information, complementary to astrometry, the apparent brightness of SSOs in the unfiltered G band is also provided for selected observations. AIMS: We explain the processing of SSO data, and describe the criteria we used to select the sample published in Gaia DR2. We then explore the data set to assess its quality. METHODS: To exploit the main data product for the solar system in Gaia DR2, which is the epoch astrometry of asteroids, it is necessary to take into account the unusual properties of the uncertainty, as the position information is nearly one-dimensional. When this aspect is handled appropriately, an orbit fit can be obtained with post-fit residuals that are overall consistent with the a-priori error model that was used to define individual values of the astrometric uncertainty. The role of both random and systematic errors is described. The distribution of residuals allowed us to identify possible contaminants in the data set (such as stars). Photometry in the G band was compared to computed values from reference asteroid shapes and to the flux registered at the corresponding epochs by the red and blue photometers (RP and BP). RESULTS: The overall astrometric performance is close to the expectations, with an optimal range of brightness G ∼ 12 − 17. In this range, the typical transit-level accuracy is well below 1 mas. For fainter asteroids, the growing photon noise deteriorates the performance. Asteroids brighter than G ∼ 12 are affected by a lower performance of the processing of their signals. The dramatic improvement brought by Gaia DR2 astrometry of SSOs is demonstrated by comparisons to the archive data and by preliminary tests on the detection of subtle non-gravitational effects