Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Design of nest access grids and perches in front of the nests: Influence on the behavior of laying hens.

In aviary systems for laying hens, it is important to provide suitable nest access platforms in front of the nests, allowing hens to reach and explore each of the nests easily. This access platform is needed to achieve good nest acceptance by the hens and thereby prevent mislaid eggs. In the present experiment, the behavior of hens using 2 different nest access platforms, a plastic grid and 2 wooden perches, was examined. Furthermore, the nests were placed on both sides of the aviary rack (corridor side and outdoor side), either integrated into the aviary rack itself (integrated nest; IN) or placed on the walls of the pens (wall nest; WN), resulting in a 2 × 2 factorial design Four thousand five hundred white laying hens were housed in 20 test pens. The eggs in the nests and mislaid eggs were collected daily, and the behavior of hens on the nest accesses was filmed during wk 25 and 26, using focal observation and scan sampling methods. More balancing, body contact, and agonistic interactions were expected for nests with perches, whereas more walking and nest inspections were expected for nests with grids. There were more mislaid eggs and balancing found in pens equipped with nests with wooden perches. More agonistic interactions and balancing, less standing, and a longer duration of nest inspection were found with the WN compared with the IN. Interactions between platform design and position of the nests were found for duration of nest visits, body contact, and walking, with the highest amount for WN equipped with plastic grids. Nests on the corridor side were favored by the hens. Nest-related behaviors, such as nest inspection, standing, and walking, decreased over time as did the number of hens on the nest accesses, whereas sitting increased. These results indicate that the hens had more difficulties in gripping the perches as designed. The lower number of hens on the nest access platforms in front of IN may be due to a better distribution around nests and tier changes within the aviary rack. Based on these results, grids rather than perches provide for improved nesting behavior.

Distortion-sensitive insight into the pretransitional behavior of 4- n -octyloxy-4′-cyanobiphenyl (8OCB)

Results of studies of the static and dynamic dielectric properties in rod-like 4-n-octyloxy-4'-cyanobiphenyl (8OCB) with isotropic (I)–nematic (N)–smectic A (SmA)–crystal (Cr) mesomorphism, combined with measurements of the low-frequency nonlinear dielectric effect and heat capacity are presented. The analysis is supported by the derivative-based and distortion-sensitive transformation of experimental data. Evidence for the I–N and N–SmA pretransitional anomalies, indicating the influence of tricritical behavior, is shown. It has also been found that neither the N phase nor the SmA phase are uniform and hallmarks of fluid–fluid crossovers can be detected. The dynamics, tested via the evolution of the primary relaxation time, is clearly non-Arrhenius and described via τ(T) = τc(T−TC)−phgr. In the immediate vicinity of the I–N transition a novel anomaly has been found: Δτ ∝ 1/(T − T*), where T* is the temperature of the virtual continuous transition and Δτ is the excess over the 'background behavior'. Experimental results are confronted with the comprehensive Landau–de Gennes theory based modeling.

The Integration of Electricity from Renewable Energy Sources in the European Union Electricity Market – The case for “Smart Grids”

The power sector is to play a central role in a low carbon economy. In all the decarbonisation scenarios of the European Union renewable energy sources (RES) will be a crucial part of the solution. Current grids constitute however major bottlenecks for the future expansion of RES. Recognising the need for a modernisation of its grids, the European Union has called for the creation of a "smart supergrid" interconnecting European grids at the continental level and making them "intelligent" through the addition of information and communication technology (ICT). To implement its agenda the EU has taken a leading role in coordinating research efforts and creating a common legislative framework for the necessary modernisation of Europe’s grids. This paper intends to give both an overview and a critical appraisal of the measures taken so far by the European Union to "transform" the grids into the backbone of a decarbonised electricity system. It suggests that if competition is to play a significant role in the deployment of smart grids, the current regulatory paradigm will have to be fundamentally reassessed

Distortion-free enhancement of terahertz signals measured by electro-optic sampling. I. Theory

We present three methods for the distortion-free enhancement of THz signals measured by electro-optic sampling in zinc blende-type detector crystals, e.g., ZnTe or GaP. A technique commonly used in optically heterodyne-detected optical Kerr effect spectroscopy is introduced, which is based on two measurements at opposite optical biases near the zero transmission point in a crossed polarizer detection geometry. In contrast to other techniques for an undistorted THz signal enhancement, it also works in a balanced detection scheme and does not require an elaborate procedure for the reconstruction of the true signal as the two measured waveforms are simply subtracted to remove distortions. We study three different approaches for setting an optical bias using the Jones matrix formalism and discuss them also in the framework of optical heterodyne detection. We show that there is an optimal bias point in realistic situations where a small fraction of the probe light is scattered by optical components. The experimental demonstration will be given in the second part of this two-paper series [J. Opt. Soc. Am. B, doc. ID 204877 (2014, posted online)].

Distortion-free enhancement of terahertz signals measured by electro-optic sampling. II. Experiment

Three methods for distortion-free enhancement of electro-optic sampling measurements of terahertz signals are tested. In the first part of this two-paper series [J. Opt. Soc. Am B 31, 904–910 (2014)], the theoretical framework for describing the signal enhancement was presented and discussed. As the applied optical bias is decreased, individual signal traces become enhanced but distorted. Here we experimentally show that nonlinear signal components that distort the terahertz electric field measurement can be removed by subtracting traces recorded with opposite optical bias values. In all three methods tested, we observe up to an order of magnitude increase in distortion-free signal enhancement, in agreement with the theory, making possible measurements of small terahertz-induced transient birefringence signals with increased signal-to-noise ratio.

Color polymorphism and sex ratio distortion in a cichlid fish as an incipient stage in sympatric speciation by sexual selection

We investigated a Lake Victoria cichlid with a complex colour polymorphism that apparently represents one original species and two incipient species, all of which are sympatric. In laboratory breeding experiments we observed sex ratio distortion in certain matings between original and incipient species. Mate choice experiments show that males of the incipient species exhibit mating preferences against the original species, and males and females of the original species exhibit strong mating preferences against the incipient species. Mating preferences might evolve by sex ratio selection to avoid matings with distorted progeny sex ratios. Phenotype frequencies in nature suggest that mating preferences translate into mating frequencies, thus restricting gene flow and exerting disruptive sexual selection between the original and incipient species. The incipient species do not differ in morphology or ecology from the original species, implying that colour polymorphism, associated with sex ratio distortion, can be an incipient stage in sympatric speciation, and that disruption of gene flow can precede ecological differentiation