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Influence of Arctic sea-ice variability on Pacific trade winds.
A conceptual model connecting seasonal loss of Arctic sea ice to midlatitude extreme weather events is applied to the 21st-century intensification of Central Pacific trade winds, emergence of Central Pacific El Nino events, and weakening of the North Pacific Aleutian Low Circulation. According to the model, Arctic Ocean warming following the summer sea-ice melt drives vertical convection that perturbs the upper troposphere. Static stability calculations show that upward convection occurs in annual 40- to 45-d episodes over the seasonally ice-free areas of the Beaufort-to-Kara Sea arc. The episodes generate planetary waves and higher-frequency wave trains that transport momentum and heat southward in the upper troposphere. Regression of upper tropospheric circulation data on September sea-ice area indicates that convection episodes produce wave-mediated teleconnections between the maximum ice-loss region north of the Siberian Arctic coast and the Intertropical Convergence Zone (ITCZ). These teleconnections generate oppositely directed trade-wind anomalies in the Central and Eastern Pacific during boreal winter. The interaction of upper troposphere waves with the ITCZ air-sea column may also trigger Central Pacific El Nino events. Finally, waves reflected northward from the ITCZ air column and/or generated by triggered El Nino events may be responsible for the late winter weakening of the Aleutian Low Circulation in recent years
Objective Bayesian analysis of neutrino masses and hierarchy
Given the precision of current neutrino data, priors still impact noticeably
the constraints on neutrino masses and their hierarchy. To avoid our
understanding of neutrinos being driven by prior assumptions, we construct a
prior that is mathematically minimally informative. Using the constructed
uninformative prior, we find that the normal hierarchy is favoured but with
inconclusive posterior odds of 5.1:1. Better data is hence needed before the
neutrino masses and their hierarchy can be well constrained. We find that the
next decade of cosmological data should provide conclusive evidence if the
normal hierarchy with negligible minimum mass is correct, and if the
uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other
hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will
be difficult with the same uncertainties. Our uninformative prior was
constructed from principles of the Objective Bayesian approach. The prior is
called a reference prior and is minimally informative in the specific sense
that the information gain after collection of data is maximised. The prior is
computed for the combination of neutrino oscillation data and cosmological data
and still applies if the data improve.Comment: 15 pages. Minor changes to match accepted version in JCA
Mathematical difficulties as decoupling of expectation and developmental trajectories
Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science
On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods
We investigate whether a Gaussian likelihood, as routinely assumed in the
analysis of cosmological data, is supported by simulated survey data. We define
test statistics, based on a novel method that first destroys Gaussian
correlations in a dataset, and then measures the non-Gaussian correlations that
remain. This procedure flags pairs of datapoints which depend on each other in
a non-Gaussian fashion, and thereby identifies where the assumption of a
Gaussian likelihood breaks down. Using this diagnostic, we find that
non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions
are significant. With a simple exclusion of the most contaminated datapoints,
the posterior for is shifted without broadening, but we find no
significant reduction in the tension with derived from Planck Cosmic
Microwave Background data. However, we also show that the one-point
distributions of the correlation statistics are noticeably skewed, such that
sound weak lensing data sets are intrinsically likely to lead to a
systematically low lensing amplitude being inferred. The detected
non-Gaussianities get larger with increasing angular scale such that for future
wide-angle surveys such as Euclid or LSST, with their very small statistical
errors, the large-scale modes are expected to be increasingly affected. The
shifts in posteriors may then not be negligible and we recommend that these
diagnostic tests be run as part of future analyses.Comment: Replacement to match accepted MNRAS versio
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