On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Characterising the three-dimensional ozone distribution of a tidally locked Earth-like planet

We simulate the 3D ozone distribution of a tidally locked Earth-like exoplanet using the high-resolution, 3D chemistry climate model CESM1(WACCM) and study how the ozone layer of a tidally locked Earth (TLE) (ΩTLE = 1/365 days) differs from that of our present-day Earth (PDE) (ΩPDE = 1/1 day). The middle atmosphere reaches a steady state a symptotically within the first 80 days of the simulation. An upwelling, centred on the subsolar point, is present on the day side while a downwelling, centred on the antisolar point, is present on the night side. In the mesosphere, we find similar global ozone distributions for the TLE and the PDE, with decreased ozone on the day side and enhanced ozone on the night side. In the lower mesosphere, a jet stream transitions into a large-scale vortex around a low-pressure system, located at low latitudes of the TLE night side. In the middle stratosphere, the concentration of odd oxygen is approximately equal to that of the ozone [(Ox) ≈ (O3)]. At these altitudes, the lifetime of odd oxygen is ~16 h and the transport processes significantly contribute to the global distribution of stratospheric ozone. Compared to the PDE, where the strong Coriolis force acts as a mixing barrier between low and high latitudes, the transport processes of the TLE are governed by jet streams variable in the zonal and meridional directions. In the middle stratosphere of the TLE, we find high ozone values on the day side, due to the increased production of atomic oxygen on the day side, where it immediately recombines with molecular oxygen to form ozone. In contrast, the ozone is depleted on the night side, due to changes in the solar radiation distribution and the presence of a downwelling. As a result of the reduced Coriolis force, the tropical and extratropical air masses are well mixed and the global temperature distribution of the TLE stratosphere has smaller horizontal gradients than the PDE. Compared to the PDE, the total ozone column global mean is reduced by ~19.3 %. The day side and the night side total ozone column means are reduced by 23.21 and 15.52 %, respectively. Finally, we present the total ozone column (TOC) maps as viewed by a remote observer for four phases of the TLE during its revolution around the star. The mean TOC values of the four phases of the TLE vary by up to 23 %.

Composition Space Analysis in the Development of Copper Molybdate Hybrids Decorated by a Bifunctional Pyrazolyl/1,2,4-Triazole Ligand

A bitopic ligand, 4-(3,5-dimethylpyrazol-4-yl)-1,2,4-triazole (Hpz-tr) (1), containing two different heterocyclic moieties was employed for the design of copper(II)–molybdate solids under hydrothermal conditions. In the multicomponent CuII/Hpz-tr/MoVI system, a diverse set of coordination hybrids, [Cu(Hpz-tr)2SO4]·3H2O (2), [Cu(Hpz-tr)Mo3O10] (3), [Cu4(OH)4(Hpz-tr)4Mo8O26]·6H2O (4), [Cu(Hpz-tr)2Mo4O13] (5), and [Mo2O6(Hpz-tr)]·H2O (6), was prepared and characterized. A systematic investigation of these systems in the form of a ternary crystallization diagram approach was utilized to show the influence of the molar ratios of starting reagents, the metal (CuII and MoVI) sources, the temperature, etc., on the reaction products outcome. Complexes 2–4 dominate throughout a wide crystallization range of the composition triangle, while the other two compounds 5 and 6 crystallize as minor phases in a narrow concentration range. In the crystal structures of 2–6, the organic ligand behaves as a short [N–N]-triazole linker between metal centers Cu···Cu in 2–4, Cu···Mo in 5, and Mo···Mo in 6, while the pyrazolyl function remains uncoordinated. This is the reason for the exceptional formation of low-dimensional coordination motifs: 1D for 2, 4, and 6 and 2D for 3 and 5. In all cases, the pyrazolyl group is involved in H bonding (H-donor/H-acceptor) and is responsible for π–π stacking, thus connecting the chain and layer structures in more complicated H-bonding architectures. These compounds possess moderate thermal stability up to 250–300 °C. The magnetic measurements were performed for 2–4, revealing in all three cases antiferromagnetic exchange interactions between neighboring CuII centers and long-range order with a net moment below Tc of 13 K for compound 4.

The immune geography of IgA induction and function

The production of immunoglobulin A (IgA) in mammals exceeds all other isotypes, and it is mostly exported across mucous membranes. The discovery of IgA and the realization that it dominates humoral mucosal immunity, in contrast to the IgG dominance of the systemic immune system, was early evidence for the distinct nature of mucosal immunology. It is now clear that IgA can function in high-affinity modes for neutralization of toxins and pathogenic microbes, and as a low-affinity system to contain the dense commensal microbiota within the intestinal lumen. The basic map of induction of IgA B cells in the Peyer's patches, which then circulate through the lymph and bloodstream to seed the mucosa with precursors of plasma cells that produce dimeric IgA for export through the intestinal epithelium, has been known for more than 30 years. In this review, we discuss the mechanisms underlying selective IgA induction of mucosal B cells for IgA production and the immune geography of their homing characteristics. We also review the functionality of secretory IgA directed against both commensal organisms and pathogens.

Reanalysis of the Hamburg Storm Surge of 1962

In February 1962, Hamburg experienced its most catastrophic storm surge event of the 20th century. This paper analyses the event using the Twentieth Century Reanalysis (20CR) dataset. Responsible for the major flood was a strong low pressure system centred over Scandinavia that was associated with strong north-westerly winds towards the German North Sea coast – the ideal storm surge situation for the Elbe estuary. A comparison of the 20CR dataset with observational data proves the applicability of the reanalysis data for this extreme event.

Quick divergence but slow convergence during ecotype formation in lake and stream stickleback pairs of variable age

When genetic constraints restrict phenotypic evolution, diversification can be predicted to evolve along so-called lines of least resistance. To address the importance of such constraints and their resolution, studies of parallel phenotypic divergence that differ in their age are valuable. Here, we investigate the parapatric evolution of six lake and stream threespine stickleback systems from Iceland and Switzerland, ranging in age from a few decades to several millennia. Using phenotypic data, we test for parallelism in ecotypic divergence between parapatric lake and stream populations and compare the observed patterns to an ancestral-like marine population. We find strong and consistent phenotypic divergence, both among lake and stream populations and between our freshwater populations and the marine population. Interestingly, ecotypic divergence in low-dimensional phenotype space (i.e. single traits) is rapid and seems to be often completed within 100 years. Yet, the dimensionality of ecotypic divergence was highest in our oldest systems and only there parallel evolution of unrelated ecotypes was strong enough to overwrite phylogenetic contingency. Moreover, the dimensionality of divergence in different systems varies between trait complexes, suggesting different constraints and evolutionary pathways to their resolution among freshwater systems.

Flood triggering in Switzerland: the role of daily to monthly preceding precipitation

Determining the role of different precipitation periods for peak discharge generation is crucial for both projecting future changes in flood probability and for short- and medium-range flood forecasting. In this study, catchment-averaged daily precipitation time series are analyzed prior to annual peak discharge events (floods) in Switzerland. The high number of floods considered – more than 4000 events from 101 catchments have been analyzed – allows to derive significant information about the role of antecedent precipitation for peak discharge generation. Based on the analysis of precipitation times series, a new separation of flood-related precipitation periods is proposed: (i) the period 0 to 1 day before flood days, when the maximum flood-triggering precipitation rates are generally observed, (ii) the period 2 to 3 days before flood days, when longer-lasting synoptic situations generate "significantly higher than normal" precipitation amounts, and (iii) the period from 4 days to 1 month before flood days when previous wet episodes may have already preconditioned the catchment. The novelty of this study lies in the separation of antecedent precipitation into the precursor antecedent precipitation (4 days before floods or earlier, called PRE-AP) and the short range precipitation (0 to 3 days before floods, a period when precipitation is often driven by one persistent weather situation like e.g., a stationary low-pressure system). A precise separation of "antecedent" and "peak-triggering" precipitation is not attempted. Instead, the strict definition of antecedent precipitation periods permits a direct comparison of all catchments. The precipitation accumulating 0 to 3 days before an event is the most relevant for floods in Switzerland. PRE-AP precipitation has only a weak and region-specific influence on flood probability. Floods were significantly more frequent after wet PRE-AP periods only in the Jura Mountains, in the western and eastern Swiss plateau, and at the outlet of large lakes. As a general rule, wet PRE-AP periods enhance the flood probability in catchments with gentle topography, high infiltration rates, and large storage capacity (karstic cavities, deep soils, large reservoirs). In contrast, floods were significantly less frequent after wet PRE-AP periods in glacial catchments because of reduced melt. For the majority of catchments however, no significant correlation between precipitation amounts and flood occurrences is found when the last 3 days before floods are omitted in the precipitation amounts. Moreover, the PRE-AP was not higher for extreme floods than for annual floods with a high frequency and was very close to climatology for all floods. The fact that floods are not significantly more frequent nor more intense after wet PRE-AP is a clear indicator of a short discharge memory of Pre-Alpine, Alpine and South Alpine Swiss catchments. Our study poses the question whether the impact of long-term precursory precipitation for floods in such catchments is not overestimated in the general perception. The results suggest that the consideration of a 3–4 days precipitation period should be sufficient to represent (understand, reconstruct, model, project) Swiss Alpine floods.

On The Breakdown Properties of some Multivariate M-Functionals

For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution-free’ M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

Validity of an automatic measure protocol in distal femur for allograft selection from a three-dimensional virtual bone bank system

Osteoarticular allograft is one possible treatment in wide surgical resections with large defects. Performing best osteoarticular allograft selection is of great relevance for optimal exploitation of the bone databank, good surgery outcome and patient’s recovery. Current approaches are, however, very time consuming hindering these points in practice. We present a validation study of a software able to perform automatic bone measurements used to automatically assess the distal femur sizes across a databank. 170 distal femur surfaces were reconstructed from CT data and measured manually using a size measure protocol taking into account the transepicondyler distance (A), anterior-posterior distance in medial condyle (B) and anterior-posterior distance in lateral condyle (C). Intra- and inter-observer studies were conducted and regarded as ground truth measurements. Manual and automatic measures were compared. For the automatic measurements, the correlation coefficients between observer one and automatic method, were of 0.99 for A measure and 0.96 for B and C measures. The average time needed to perform the measurements was of 16 h for both manual measurements, and of 3 min for the automatic method. Results demonstrate the high reliability and, most importantly, high repeatability of the proposed approach, and considerable speed-up on the planning.

Nonlinear three-dimensional noise filter with low-dose CT angiography: effect on the detection of small high-contrast objects in a phantom model

To study the effect of a nonlinear noise filter on the detection of simulated endoleaks in a phantom with 80- and 100-kVp multidetector computed tomographic (CT) angiography.

Full body low radiation radiography using Lodox Statscan

Lodox Statscan provides high-speed, high-quality, low radiation, full body imaging in a single scan, combined with three-dimensional reconstructive and zooming functionality. Several trauma centres have incorporated it into their advanced trauma life support protocol. This review gives a brief overview of the system.