We study second-order partial differential equations (PDEs) in four dimensions for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge–Ampère property. Since half-flatness of the conformal structure is equivalent to the existence of a non-trivial dispersionless ...

We give a simple criterion for the cyclicity of the m-torsion subgroup of the group of rational points on an elliptic curve defined over a finite field of characteristic larger than 3 for m = 2, 3, 4, 6, 12.

Knowledge about frequency and location of snow avalanche activity is essential for forecasting and mapping of snow avalanche hazard. Traditional field monitoring of avalanche activity has limitations, especially when surveying large and remote areas. In recent years, avalanche detection in Sentinel-1 radar satellite imagery has been developed to improve monitoring. However, the current state-of-the-art ...

Classical assessments of trends in gridded temperature data perform independent evaluations across the grid, thus, ignoring spatial correlations in the trend estimates. In particular, this affects assessments of trend significance as evaluation of the collective significance of individual tests is commonly neglected. In this article we build a space–time hierarchical Bayesian model for temperature ...

High-density lipoproteins (HDL) are a heterogenous group of plasma molecules with a large variety in composition. There is a wide specter in lipid content and the number of different proteins that has been associated with HDL is approaching 100. Given this heterogeneity and the fact that the total amount of HDL is inversely related to the risk of coronary heart disease (CHD), there has been ...

The spatiotemporal temperature variability for several gridded instrumental and general circulation climate model data is characterized, contrasting power spectra of local and global temperatures, land and sea temperatures, and temperatures of different regions. There is generally a high degree of agreement between the spectral characteristics of instrumental and climate model data. All but the ...

We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context. This involves, in particular, a new definition of strong characteristicity. The proof exploits a spectral sequence relating ...

Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We ...

Various interpretations of the notion of a trend in the context of global warming are discussed, contrasting the difference between viewing a trend as the deterministic response to an external forcing and viewing it as a slow variation which can be separated from the background spectral continuum of long-range persistent climate noise. The emphasis in this paper is on the latter notion, and a ...