Compatibility of the method of brackets with classical integration rules

International audienceThe method of brackets is a symbolic approach to the computation of integrals over R n {{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years. This article shows that this method is consistent with most classical rules for the computation of integrals, such as the fundamental theorem of calculus, the Laplace transform, the reduction formula for the integration of functions with spherical symmetry, the Cauchy-Schlömilch transformation, and explicit evaluations for multivariate integrals of product of Bessel functions as obtained by Exton and Srivastava. This work is part of a program dedicated to the derivation of solid theoretical grounds for the use of this attractive integration method

Benefits of plant strips for sustainable mountain agriculture

Erosion degrades soil quality in agricultural ecosystems, thereby reducing the productivity of the land. Semi-natural vegetation and diverse cropping systems have been converted into monocultures with low tree densities, leaving the soil unprotected. We evaluated the association in soil- and water-conservation systems with production in traditional almond orchards and the beneficial impact of plant strips in mountainous agriculture. Soil loss, runoff and nutrient loss over a four-year period (2002–2005) were monitored in hillside erosion plots with almond trees under different soil-management systems: (1) non-tillage with sage (Salvia lavandulifolia L. subspecies Oxyodon) strips 3 m wide; (2) non-tillage with rosemary (Rosmarinus officinalis L.) strips, (3) non-tillage with thyme (Thymus baeticus L. Boiss. exlacaita) strips, and (4) conventional tillage on the south flank of the Sierra Nevada (Lanjaron) in south-eastern Spain. Also, the nut yield from almond trees, and the biomass from aromatic-shrub strips were measured. The erosion plots, located on a 35% slope, were 144 m$^{2}$ in area. The plant-cover strips, 3 m wide, ran across the slope. Our results show that the most effective treatment proved to be non-tillage with thyme strips, reducing the annual soil loss by 93% and runoff by 80%, with respect to conventional tillage. Non-tillage with rosemary strips reduced soil loss by 91% and runoff by 82%, with respect to conventional tillage, while these percentages were 69% and 51%, respectively, for non-tillage with sage strips. In addition, all the treatments as a whole, in comparison with conventional tillage, revealed that the plant strips were the decisive factor in the reduction of NPK losses by surface runoff. The average nut yield from non-tillage with sage strips, non-tillage with rosemary strips, non-tillage with thyme strips and conventional tillage during the study period was 2.4, 3.2, 3.8 and 4.5 kg tree$^{-1}$, respectively, and the essential oil yield from sage, rosemary and thyme strips was 5.0, 8.7 and 10.8 L ha$^{-1}$, respectively. The non-tillage with thyme strips decreased nutrient loading in surface waters and thus had a positive impact on the environment while simultaneously maintaining reasonable almond-production levels. Thus, the combination of orchard trees with shrubs provided a viable option to conserve soil and water in hilly areas with opportunities to increase overall land productivity as well as sustainable agro-environmental measures

The PLATO Mission

International audiencePLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases

The PLATO Mission

International audiencePLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases

Health-status outcomes with invasive or conservative care in coronary disease

BACKGROUND In the ISCHEMIA trial, an invasive strategy with angiographic assessment and revascularization did not reduce clinical events among patients with stable ischemic heart disease and moderate or severe ischemia. A secondary objective of the trial was to assess angina-related health status among these patients. METHODS We assessed angina-related symptoms, function, and quality of life with the Seattle Angina Questionnaire (SAQ) at randomization, at months 1.5, 3, and 6, and every 6 months thereafter in participants who had been randomly assigned to an invasive treatment strategy (2295 participants) or a conservative strategy (2322). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate differences between the treatment groups. The primary outcome of this health-status analysis was the SAQ summary score (scores range from 0 to 100, with higher scores indicating better health status). All analyses were performed in the overall population and according to baseline angina frequency. RESULTS At baseline, 35% of patients reported having no angina in the previous month. SAQ summary scores increased in both treatment groups, with increases at 3, 12, and 36 months that were 4.1 points (95% credible interval, 3.2 to 5.0), 4.2 points (95% credible interval, 3.3 to 5.1), and 2.9 points (95% credible interval, 2.2 to 3.7) higher with the invasive strategy than with the conservative strategy. Differences were larger among participants who had more frequent angina at baseline (8.5 vs. 0.1 points at 3 months and 5.3 vs. 1.2 points at 36 months among participants with daily or weekly angina as compared with no angina). CONCLUSIONS In the overall trial population with moderate or severe ischemia, which included 35% of participants without angina at baseline, patients randomly assigned to the invasive strategy had greater improvement in angina-related health status than those assigned to the conservative strategy. The modest mean differences favoring the invasive strategy in the overall group reflected minimal differences among asymptomatic patients and larger differences among patients who had had angina at baseline

Initial invasive or conservative strategy for stable coronary disease

BACKGROUND Among patients with stable coronary disease and moderate or severe ischemia, whether clinical outcomes are better in those who receive an invasive intervention plus medical therapy than in those who receive medical therapy alone is uncertain. METHODS We randomly assigned 5179 patients with moderate or severe ischemia to an initial invasive strategy (angiography and revascularization when feasible) and medical therapy or to an initial conservative strategy of medical therapy alone and angiography if medical therapy failed. The primary outcome was a composite of death from cardiovascular causes, myocardial infarction, or hospitalization for unstable angina, heart failure, or resuscitated cardiac arrest. A key secondary outcome was death from cardiovascular causes or myocardial infarction. RESULTS Over a median of 3.2 years, 318 primary outcome events occurred in the invasive-strategy group and 352 occurred in the conservative-strategy group. At 6 months, the cumulative event rate was 5.3% in the invasive-strategy group and 3.4% in the conservative-strategy group (difference, 1.9 percentage points; 95% confidence interval [CI], 0.8 to 3.0); at 5 years, the cumulative event rate was 16.4% and 18.2%, respectively (difference, 121.8 percentage points; 95% CI, 124.7 to 1.0). Results were similar with respect to the key secondary outcome. The incidence of the primary outcome was sensitive to the definition of myocardial infarction; a secondary analysis yielded more procedural myocardial infarctions of uncertain clinical importance. There were 145 deaths in the invasive-strategy group and 144 deaths in the conservative-strategy group (hazard ratio, 1.05; 95% CI, 0.83 to 1.32). CONCLUSIONS Among patients with stable coronary disease and moderate or severe ischemia, we did not find evidence that an initial invasive strategy, as compared with an initial conservative strategy, reduced the risk of ischemic cardiovascular events or death from any cause over a median of 3.2 years. The trial findings were sensitive to the definition of myocardial infarction that was used