First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Measurements of stratospheric ozone at a mid-latitude observing station Valentia, Ireland (51.94° N, 10.25° W), using ground-based and ozonesonde observations from 1994 to 2009

Sixteen years (1994 – 2009) of ozone profiling by ozonesondes at Valentia Meteorological and Geophysical Observatory, Ireland (51.94° N, 10.23° W) along with a co-located MkIV Brewer spectrophotometer for the period 1993–2009 are analyzed. Simple and multiple linear regression methods are used to infer the recent trend, if any, in stratospheric column ozone over the station. The decadal trend from 1994 to 2010 is also calculated from the monthly mean data of Brewer and column ozone data derived from satellite observations. Both of these show a 1.5 % increase per decade during this period with an uncertainty of about ±0.25 %. Monthly mean data for March show a much stronger trend of ~ 4.8 % increase per decade for both ozonesonde and Brewer data. The ozone profile is divided between three vertical slots of 0–15 km, 15–26 km, and 26 km to the top of the atmosphere and a 11-year running average is calculated. Ozone values for the month of March only are observed to increase at each level with a maximum change of +9.2 ± 3.2 % per decade (between years 1994 and 2009) being observed in the vertical region from 15 to 26 km. In the tropospheric region from 0 to 15 km, the trend is positive but with a poor statistical significance. However, for the top level of above 26 km the trend is significantly positive at about 4 % per decade. The March integrated ozonesonde column ozone during this period is found to increase at a rate of ~6.6 % per decade compared with the Brewer and satellite positive trends of ~5 % per decade.

Temperature-dependent reduction pathways of complexes fac-[Re(CO)3(N-R-imidazole)(1,10-phenanthroline)]+ (R = H, CH3)

Peculiar reduction pathways of the complexes fac-[Re(imH)(CO)3(phen)]+ and fac-[Re(imCH3)(CO)3(phen)]+ (imH = imidazole, imCH3 = N-methylimidazole and phen = 1,10-phenanthroline) have been unravelled by performing combined cyclic voltammetric and in situ IR spectroelectrochemical experiments. In the temperature range of 293–233 K, the initial reduction of the phen ligand in [Re(imH)(CO)3(phen)]+ results in irreversible conversion of the imidazole ligand to 3-imidazolate by a rapid phen•−→ imH intramolecular electron transfer coupled with N H bond cleavage. This process is followed by second phen-localized 1e− reduction producing [ReI(3-im−)(CO)3(phen•−)]−, similar to the analogous 2,2'-bipyridine complex. In contrast to the bpy analogue, the stability of the phen•−-containing complexes is significantly affected by lowering the temperature. At 233 K, a secondary reaction occurs in both [Re(3-im−)(CO)3(phen•−)]− and [Re(imCH3)(CO)3(phen•−)]. The resulting products exhibit v(CO) wavenumbers indistinguishable from those of the parent phen•− complexes; however, their oxidation occurs at a considerably more positive electrode potential. It is proposed that these species are produced by a new C C bond formation between the C(2) site of 3-im− or imCH3 and the C(2) site of the phen•−ligand.

K-Surfer: a KNIME extension for the management and analysis of Human brain MRI FreeSurfer/FSL data

Human brain imaging techniques, such as Magnetic Resonance Imaging (MRI) or Diffusion Tensor Imaging (DTI), have been established as scientific and diagnostic tools and their adoption is growing in popularity. Statistical methods, machine learning and data mining algorithms have successfully been adopted to extract predictive and descriptive models from neuroimage data. However, the knowledge discovery process typically requires also the adoption of pre-processing, post-processing and visualisation techniques in complex data workflows. Currently, a main problem for the integrated preprocessing and mining of MRI data is the lack of comprehensive platforms able to avoid the manual invocation of preprocessing and mining tools, that yields to an error-prone and inefficient process. In this work we present K-Surfer, a novel plug-in of the Konstanz Information Miner (KNIME) workbench, that automatizes the preprocessing of brain images and leverages the mining capabilities of KNIME in an integrated way. K-Surfer supports the importing, filtering, merging and pre-processing of neuroimage data from FreeSurfer, a tool for human brain MRI feature extraction and interpretation. K-Surfer automatizes the steps for importing FreeSurfer data, reducing time costs, eliminating human errors and enabling the design of complex analytics workflow for neuroimage data by leveraging the rich functionalities available in the KNIME workbench.

Re-examining the U.K.'s greatest tornado outbreak: forecasting the limited extent of tornadoes along a cold front

On 23 November 1981, a strong cold front swept across the U.K., producing tornadoes from the west to the east coasts. An extensive campaign to collect tornado reports by the Tornado and Storm Research Organisation (TORRO) resulted in 104 reports, the largest U.K. outbreak. The front was simulated with a convection-permitting numerical model down to 200-m horizontal grid spacing to better understand its evolution and meteorological environment. The event was typical of tornadoes in the U.K., with convective available potential energy (CAPE) less than 150 J kg-1, 0-1-km wind shear of 10-20 m s-1, and a narrow cold-frontal rainband forming precipitation cores and gaps. A line of cyclonic absolute vorticity existed along the front, with maxima as large as 0.04 s-1. Some hook-shaped misovortices bore kinematic similarity to supercells. The narrow swath along which the line was tornadic was bounded on the equatorward side by weak vorticity along the line and on the poleward side by zero CAPE, enclosing a region where the environment was otherwise favorable for tornadogenesis. To determine if the 104 tornado reports were plausible, first possible duplicate reports were eliminated, resulting in as few as 58 tornadoes to as many as 90. Second, the number of possible parent misovortices that may have spawned tornadoes is estimated from model output. The number of plausible tornado reports in the 200-m grid-spacing domain was 22 and as many as 44, whereas the model simulation was used to estimate 30 possible parent misovortices within this domain. These results suggest that 90 reports was plausible.