Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

ON SOME GEOMETRY OF PROPAGATION IN DIFFRACTIVE TIME SCALES

International audienceIn this article, we develop a non linear geometric optics which presents the two main following features. It is valid in diffractive times and it extends the classical approaches to the case of fast variable coefficients. In this context, we can show that the energy is transported along the rays associated with some non usual long-time hamiltonian. Our analysis needs structural assumptions and initial data suitably polrarized to be implemented. All the required conditions are met concerning a current model arising in fluid mechanics and which was the original motivation of our work. As a by product, we get results complementary to the litterature concerning the propagation of the Rossby waves which play a part in the description of large oceanic currents, like Gulf stream or Kuroshio

Variability in the analysis of a single neuroimaging dataset by many teams

Data analysis workflows in many scientific domains have become increasingly complex and flexible. To assess the impact of this flexibility on functional magnetic resonance imaging (fMRI) results, the same dataset was independently analyzed by 70 teams, testing nine ex-ante hypotheses. The flexibility of analytic approaches is exemplified by the fact that no two teams chose identical workflows to analyze the data. This flexibility resulted in sizeable variation in hypothesis test results, even for teams whose statistical maps were highly correlated at intermediate stages of their analysis pipeline. Variation in reported results was related to several aspects of analysis methodology. Importantly, meta-analytic approaches that aggregated information across teams yielded significant consensus in activated regions across teams. Furthermore, prediction markets of researchers in the field revealed an overestimation of the likelihood of significant findings, even by researchers with direct knowledge of the dataset. Our findings show that analytic flexibility can have substantial effects on scientific conclusions, and demonstrate factors related to variability in fMRI. The results emphasize the importance of validating and sharing complex analysis workflows, and demonstrate the need for multiple analyses of the same data. Potential approaches to mitigate issues related to analytical variability are discussed

Variability in the analysis of a single neuroimaging dataset by many teams

Data analysis workflows in many scientific domains have become increasingly complex and flexible. To assess the impact of this flexibility on functional magnetic resonance imaging (fMRI) results, the same dataset was independently analyzed by 70 teams, testing nine ex-ante hypotheses. The flexibility of analytic approaches is exemplified by the fact that no two teams chose identical workflows to analyze the data. This flexibility resulted in sizeable variation in hypothesis test results, even for teams whose statistical maps were highly correlated at intermediate stages of their analysis pipeline. Variation in reported results was related to several aspects of analysis methodology. Importantly, meta-analytic approaches that aggregated information across teams yielded significant consensus in activated regions across teams. Furthermore, prediction markets of researchers in the field revealed an overestimation of the likelihood of significant findings, even by researchers with direct knowledge of the dataset. Our findings show that analytic flexibility can have substantial effects on scientific conclusions, and demonstrate factors related to variability in fMRI. The results emphasize the importance of validating and sharing complex analysis workflows, and demonstrate the need for multiple analyses of the same data. Potential approaches to mitigate issues related to analytical variability are discussed

Quasaprove network: a trace elements fluxes study (As, Cd, Cu, Pb, Zn) at field scale

Trace element (TE) accumulation in agricultural soils may have long-term implications for crops quality. Input of organic or chemical fertilizers is one of the major sources of TE in agricultural systems, due to their composition and the quantities involved. However, the balance with TE exported by crops is not well known and these fluxes need to be calculated to predict the potential future contamination of soils. The aims of our study were (1) to quantify TE contents in soil, plants, organic and chemical fertilizers, (2) to estimate their fluxes at field scale and (3) to compare the impact of different farming systems. On the whole French territory, a network of 90 plots in conventional or organic farming was built (QUASAPROVE). Three different types of fertilization were used: nitrate (N) fertilization, nitrate-phosphate-potassium (NPK) fertilization or organic fertilization. The plots were cultivated with sunflower, durum wheat or common wheat. The soil surface horizons (0-30 cm), fertilizers and crops were sampled and analysed for their contents of arsenic, cadmium, copper, lead and zinc. The TE inputs and exports were calculated. Atmospheric inputs and leaching were disregarded in order to focus on the impact of agricultural practices. All fertilizers showed low concentrations in TE, except for phosphate fertilizers which appeared to have the highest TE concentrations and were the main source of arsenic, cadmium, copper and zinc in conventional farming. For organic fertilizers, concentrations were low except for lead in some cases but the amount applied generates a significant inflow in TE. Whatever the cultivated crop, the balance is determined by the type of fertilization. In the case of N fertilization only, the balance is always negative for the five trace elements. In the case of organic fertilisation, for both conventional and organic farming, the balance is always positive and the soil accumulates the five trace elements. In the case of conventional farming with NPK fertilization, the balance is positive for arsenic, cadmium and lead, and negative for copper and zinc. Using repeated NPK and organic fertilization over multiple years will induce an accumulation in soils. For example, the cadmium concentration could double in soils with low initial concentration, after 120 years of annual applications of phosphate fertilizer. However the effects on the bioavailability of TE could also be modified by these inputs, especially in the case of organic inputs. The characterisation of TE bioavailability will be studied on the different soils of the QUASAPROVE network using soil solution extractions and passive samplers (DGT)

Quasaprove network: a trace elements fluxes study (As, Cd, Cu, Pb, Zn) at field scale

Trace element (TE) accumulation in agricultural soils may have long-term implications for crops quality. Input of organic or chemical fertilizers is one of the major sources of TE in agricultural systems, due to their composition and the quantities involved. However, the balance with TE exported by crops is not well known and these fluxes need to be calculated to predict the potential future contamination of soils. The aims of our study were (1) to quantify TE contents in soil, plants, organic and chemical fertilizers, (2) to estimate their fluxes at field scale and (3) to compare the impact of different farming systems. On the whole French territory, a network of 90 plots in conventional or organic farming was built (QUASAPROVE). Three different types of fertilization were used: nitrate (N) fertilization, nitrate-phosphate-potassium (NPK) fertilization or organic fertilization. The plots were cultivated with sunflower, durum wheat or common wheat. The soil surface horizons (0-30 cm), fertilizers and crops were sampled and analysed for their contents of arsenic, cadmium, copper, lead and zinc. The TE inputs and exports were calculated. Atmospheric inputs and leaching were disregarded in order to focus on the impact of agricultural practices. All fertilizers showed low concentrations in TE, except for phosphate fertilizers which appeared to have the highest TE concentrations and were the main source of arsenic, cadmium, copper and zinc in conventional farming. For organic fertilizers, concentrations were low except for lead in some cases but the amount applied generates a significant inflow in TE. Whatever the cultivated crop, the balance is determined by the type of fertilization. In the case of N fertilization only, the balance is always negative for the five trace elements. In the case of organic fertilisation, for both conventional and organic farming, the balance is always positive and the soil accumulates the five trace elements. In the case of conventional farming with NPK fertilization, the balance is positive for arsenic, cadmium and lead, and negative for copper and zinc. Using repeated NPK and organic fertilization over multiple years will induce an accumulation in soils. For example, the cadmium concentration could double in soils with low initial concentration, after 120 years of annual applications of phosphate fertilizer. However the effects on the bioavailability of TE could also be modified by these inputs, especially in the case of organic inputs. The characterisation of TE bioavailability will be studied on the different soils of the QUASAPROVE network using soil solution extractions and passive samplers (DGT)