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

The coming crisis of cultural engagement? Measurement, methods, and the nuances of niche activities

Do ticketing data and national survey data on attendance tell the same story? This question is particularly important in the context of debates over the power of new forms of data to supplant the “traditional” survey methods that have underpinned our understanding of the social stratification of culture. This paper compares three data sources on attendance: the Active Lives Survey, the Taking Part Survey, and Audience Finder. We first compare self-reported attendance at events in each English local authority from the Active Lives survey with ticket sales data, finding a close relationship. We follow up by comparing the distributions of ticket buyers across the Indices of Multiple Deprivation with those from Taking Part, finding that for widely-ticketed and widely-attended art forms they track closely together, providing support for existing trends. Ticketing data does not seem to offer more information on social stratification than traditional social science sources. However, we extend the comparison through more detailed analysis of subcategories within less well-researched forms – literature and dance events – where numbers of attendees are lower, with accompanying uncertainty in survey sources. We find that the audiences for dance vary widely, with ballet attendance being heavily socially stratified but attendance at contemporary dance much more similar to the general population. However, we find that audiences for literature events are more heavily socially stratified than almost any other art form, almost regardless of the subcategory. The power of new datasets is in offering specificity about artforms, rather than overturning what we know about culture and inequality

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

Construction d'un spectrofluorimètre corrigé en analyse et en excitation

Nous avons construit un spectrofluorimètre réalisant une correction automatique au niveau de l'excitation et de l'analyse. L'énergie de la lumière d'excitation est maintenue constante au niveau de la cellule de fluorescence par l'utilisation d'une thermopile. Les variations de la fonction d'appareil du système d'analyse sont compensées au niveau de l'enregistrement du signal de fluorescence

Construction d'un spectrofluorimètre corrigé en analyse et en excitation

A spectrofluorimeter has been achieved which performs automatic corrections relatively to excitation and analysis. The excitation light falling on the fluorescence cell has an energy kept constant with a thermopile. The variations of the sensibility of analysis apparatus are compensated when recording fluorescence signal.Nous avons construit un spectrofluorimètre réalisant une correction automatique au niveau de l'excitation et de l'analyse. L'énergie de la lumière d'excitation est maintenue constante au niveau de la cellule de fluorescence par l'utilisation d'une thermopile. Les variations de la fonction d'appareil du système d'analyse sont compensées au niveau de l'enregistrement du signal de fluorescence