Cubature formulas for symmetric measures in higher dimensions with few points

We study cubature formulas for -dimensional integrals with an arbitrary symmetric weight function of product form. We present a construction that yields a high polynomial exactness: for fixed degree or and large dimension the number of knots is only slightly larger than the lower bound of Möller and much smaller compared to the known constructions.

We also show, for any odd degree , that the minimal number of points is almost independent of the weight function. This is also true for the integration over the (Euclidean) sphere.

     

The conserved protein kinase-A target motif in synapsin of Drosophila is effectively modified by pre-mRNA editing

Background  

Synapsins are abundant synaptic vesicle associated phosphoproteins that are involved in the fine regulation of neurotransmitter release. The Drosophila member of this protein family contains three conserved domains (A, C, and E) and is expressed in most or all synaptic terminals. Similar to mouse mutants, synapsin knock-out flies show no obvious structural defects but are disturbed in complex behaviour, notably learning and memory.     

On Preservation Theorems for Two-Variable Logic

We show that the existential preservation theorem fails for two-variable first-order logic FO². It is known that for all k ≥ 3, FO^k does not have an existential preservation theorem, so this settles the last open case, answering a question of Andreka, van Benthem, and Németi. In contrast, we prove that the homomorphism preservation theorem holds for FO².     

Combined use of small-angle neutron scattering and atom probe tomography for the analysis of precipitates in a Fe-15 m% Co-25 m% Mo alloy

Atom probe tomography (APT) measurements were conducted to analyze nm-sized precipitates in a Fe-25 m% Co-15 m% Mo model alloy. Calculation of isoconcentration surfaces and application of cluster-search algorithms yielded the chemical compositions of matrix and precipitates. Small-angle neutron scattering (SANS) was performed in order to calculate the ratio of magnetic to nuclear scattering. This so-called A-ratio was compared with values calculated from the chemical information derived from the atom probe data. For this, the magnetism of the precipitates has to be taken into account. Ab-initio studies have been carried out to determine the magnetic moment of the precipitate phase. The results show that the extremely fine precipitates are ferromagnetic and exhibit near-equilibrium composition. In the very early stage of decomposition, however, the composition is different from near-equilibrium. The influences of the magnetism of the precipitates as well as of artifacts from atom probe measurements on the obtained results are discussed.     

Helfrich repulsion and dynamical phase separation of multicomponent lipid bilayers

Thermal fluctuations of surfactant bilayers in an aqueous solution produce an effective, long-range repulsion that can lead to a continuous unbinding transition. We report on an optical interferometry study of the thermal fluctuations of multicomponent bilayers close to the unbinding transition. We find that, in contrast to the case of single-component bilayers, the thermal fluctuation spectrum of multicomponent bilayers does not agree with a continuous unbinding transition but instead indicates the proximity of an unbinding tricritical point.     

Two-component Bose-Einstein condensates with a large number of vortices

We consider the condensate wave function of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of (87)Rb or (23)Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of sqrt[3], and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.