Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion

We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane

Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of $\mathbb{R}^n$ affect the sizes of the images of sets of Hausdorff dimension less than $n$. We measure the sizes of the image sets in terms of generalized Hausdorff measures

S6S^6 and the geometry of nearly K\"ahler 66-manifolds

We review results on and around the almost complex structure on $S^6$, both from a classical and a modern point of view. These notes have been prepared for the Workshop "(Non)-existence of complex structures on $S^6$" (\emph{Erste Marburger Arbeitsgemeinschaft Mathematik -- MAM-1}), held in Marburg in March 2017.Comment: 12 page

Extending the dynamic range of transcription factor action by translational regulation

A crucial step in the regulation of gene expression is binding of transcription factor (TF) proteins to regulatory sites along the DNA. But transcription factors act at nanomolar concentrations, and noise due to random arrival of these molecules at their binding sites can severely limit the precision of regulation. Recent work on the optimization of information flow through regulatory networks indicates that the lower end of the dynamic range of concentrations is simply inaccessible, overwhelmed by the impact of this noise. Motivated by the behavior of homeodomain proteins, such as the maternal morphogen Bicoid in the fruit fly embryo, we suggest a scheme in which transcription factors also act as indirect translational regulators, binding to the mRNA of other transcription factors. Intuitively, each mRNA molecule acts as an independent sensor of the TF concentration, and averaging over these multiple sensors reduces the noise. We analyze information flow through this new scheme and identify conditions under which it outperforms direct transcriptional regulation. Our results suggest that the dual role of homeodomain proteins is not just a historical accident, but a solution to a crucial physics problem in the regulation of gene expression.Comment: 14 pages, 5 figure

Order and Creep in Flux Lattices and CDWs Pinned by Planar Defects

The influence of randomly distributed point impurities \emph{and} planar defects on the order and transport in type-II superconductors and related systems is considered theoretically. For planar defects of identical orientation the flux line lattice exhibits a new glassy phase dominated by the planar defects with a finite compressibility, a transverse Meissner effect, large sample to sample fuctuations of the susceptibility and an exponential decay of translational long range order. The flux creep resistivity for currents $J$ parallel to the defects is $\rho(J)\sim \exp-(J_0/J)^{3/2}$ . Strong disorder enforces an array of dislocations to relax shear strain

Sensitive and broadband measurement of dispersion in a cavity using a Fourier transform spectrometer with kHz resolution

Optical cavities provide high sensitivity to dispersion since their resonance frequencies depend on the index of refraction. We present a direct, broadband, and accurate measurement of the modes of a high finesse cavity using an optical frequency comb and a mechanical Fourier transform spectrometer with a kHz-level resolution. We characterize 16000 cavity modes spanning 16 THz of bandwidth in terms of center frequency, linewidth, and amplitude. We retrieve the group delay dispersion of the cavity mirror coatings and pure N${_2}$ with 0.1 fs${^2}$ precision and 1 fs${^2}$ accuracy, as well as the refractivity of the 3{\nu}1+{\nu}3 absorption band of CO${_2}$ with 5 x 10${^{-12}}$ precision. This opens up for broadband refractive index metrology and calibration-free spectroscopy of entire molecular bands

The Effect of Randomness on the Mott State

We reinvestigate the competition between the Mott and the Anderson insulator state in a one-dimensional disordered fermionic system by a combination of instanton and renormalization group methods. Tracing back both the compressibility and the ac-conductivity to a vanishing kink energy of the electronic displacement field we do not find any indication for the existence of an intermediate (Mott glass) phase.Comment: 4 page

Finding space to grow urban hedges as a natural air filter along pedestrian paths: a GIS‑based investigation of a UK urban centre

Road vehicles are a significant source of air pollution in cities, with impacts on human health. Previous work has shown that hedges located between the road carriageway and pavement can help to mitigate the impact of vehicle emissions for pedestrians and residents. For continuous improvement of air quality around the city centre area, roadside hedges can be of value. This study has used UK government statistics to map the traffic emissions along major roads in an urban centre. Using appropriate geoprocessing techniques, suitable locations for planting roadside hedges have been identified along these roads. It is envisaged that planting suitable urban hedges at these locations can help further improve air quality

Design and development of a generic spatial decision support system, based on artificial intelligence and multicriteria decision analysis

A new integrated and generic Spatial Decision Support System (SDSS) is presented based on a combination of Artificial Intelligence and Multicriteria Decision Analysis techniques. The approach proposed is developed to address commonly faced spatial decision problems of site selection, site ranking, impact assessment and spatial knowledge discovery under one system. The site selection module utilises a theme-based Analytical Hierarchy Process. Two novel site ranking techniques are introduced. The first is based on a systematic neighbourhood comparison of sites with respect to key datasets (criterions). The second utilises multivariate ordering capability of one-dimensional Self-Organizing Maps. The site impact assessment module utilises a new spatially enabled Rapid Impact Assessment Matrix. A spatial variant of General Regression Neural Networks is developed for Geographically Weighted Regression (GWR) and prediction analysis. The developed system is proposed as a useful modern tool that facilitates quantitative and evidence based decision making in multicriteria decision environment. The intended users of the system are decision makers in government organisations, in particular those involved in planning and development when taking into account socio-economic, environmental and public health related issues

Geographical General Regression Neural Network (GGRNN) tool for geographically weighted regression analysis

This paper presents a new geographically weighted regression analysis tool, based upon a modified version of a General Regression Neural Network (GRNN). The new Geographic General Regression Neural Network (GGRNN) tool allows for local variations in the regression analysis. The algorithm of the GRNN has been extended to allow for both globally independent variables and local variables, restricted to a given spatial kernel. This mimics the results of Geographically Weighted Regression (GWR) analysis in a given geographical space. The GGRNN tool allows the user to load geographic data from the Shapefile into the underlying neural networks data structure. The spatial kernel can be either a fixed radius or adaptive, by using a given number of neighboring regions. The Holdout Method has been used to compare the fitness of a given model. An application of the tool has been presented using the benchmark working-age deaths in the Tokyo metropolitan area, Japan. Standardized residual maps produced by the GGRNN tool have been compared with those produced by the GWR4 tool for validation. The tool has been developed in the .Net C# programming language using the DotSpatial open source library. The tool is valuable because it allows the user to investigate the influence of spatially non-stationary processes in the regression analysis. The tool can also be used for prediction or interpolation purposes for a range of environmental, socioeconomic and public health applications