An Ostrowski type inequality in two dimensions using the three point rule

An Ostrowski Type inequality in two dimensions for double integrals on a rectangle is developed. The resulting integral inequalities are valid for the class of functions with bounded first derivatives. They are employed to approximate the double integral by up to 6 one dimensional integrals and nine functions evaluations. Examples using the resulting cubature formulae are presented

On weighted three point quadrature rules

Weighted three point quadrature rules are obtained in the current work giving explicit a priori bounds on the error. The results are valid for general weight functions. The robustness of the bounds are explored for specific weight functions and for a variety of integrands. A comparison of the current development is made with traditional quadrature rules and it is demonstrated that the current development has some advantages. In particular, this method allows the nodes and weights of an n point rule to be easily obtained, which may be preferential if the region of integration varies. Other explicit error bounds may be obtained in advance, thus making it possible to determine the partition required to achieve a certain error tolerance

Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Demoulin equilibrium

CONTEXT: As the coronal magnetic field can usually not be measured directly, it has to be extrapolated from photospheric measurements into the corona. AIMS: We test the quality of a non-linear force-free coronal magnetic field extrapolation code with the help of a known analytical solution. METHODS: The non-linear force-free equations are numerically solved with the help of an optimization principle. The method minimizes an integral over the force-free and solenoidal condition. As boundary condition we use either the magnetic field components on all six sides of the computational box in Case I or only on the bottom boundary in Case II. We check the quality of the reconstruction by computing how well force-freeness and divergence-freeness are fulfilled and by comparing the numerical solution with the analytical solution. The comparison is done with magnetic field line plots and several quantitative measures, like the vector correlation, Cauchy Schwarz, normalized vector error, mean vector error and magnetic energy. RESULTS: For Case I the reconstructed magnetic field shows good agreement with the original magnetic field topology, whereas in Case II there are considerable deviations from the exact solution. This is corroborated by the quantitative measures, which are significantly better for Case I. CONCLUSIONS: Despite the strong nonlinearity of the considered force-free equilibrium, the optimization method of extrapolation is able to reconstruct it; however, the quality of reconstruction depends significantly on the consistency of the input data, which is given only if the known solution is provided also at the lateral and top boundaries, and on the presence or absence of flux concentrations near the boundaries of the magnetogram.Comment: 6 pages, 2 figures, Research Not

DEVELOPING A METHODOLOGICAL FRAMEWORK FOR THE PARTICIPATORY MEASUREMENT OF SUSTAINABILITY

The measurement of sustainability can provide significant information in order to plan and implement environmental policies. Several methods have been proposed in the literature in order to select the appropriate indicators along with a variety of techniques for their measurement. These methods are often divided in two main categories: a) a top-down approach where the selection of sustainability indicators is often based on the decision of scientists and policy-makers and b) a bottom-up approach where local stakeholders influence the selection and the measurement of indicators. In this paper we propose a methodological framework which allows the selection of sustainability indicators based on scientific research but at the same time allows citizens to influence both the selection of indicators and their measurement. The benefits of the specific methodological framework are two: a) to incorporate in different stages of the measurement the opinions of local stakeholders, b) to assist in policy decision-making through the assessment of the current situation of sustainability

Nonlinear force-free reconstruction of the global solar magnetic field: methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday's equation, give rise to a respective normal field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modelled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition - the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic

Citrobacter rodentium induces rapid and unique metabolic and inflammatory responses in mice suffering from severe disease.

The mouse pathogen Citrobacter rodentium is used to model infections with enterohaemorrhagic and enteropathogenic Escherichia coli (EHEC and EPEC). Pathogenesis is commonly modelled in mice developing mild disease (e.g., C57BL/6). However, little is known about host responses in mice exhibiting severe colitis (e.g., C3H/HeN), which arguably provide a more clinically relevant model for human paediatric enteric infection. Infection of C3H/HeN mice with C. rodentium results in rapid colonic colonisation, coinciding with induction of key inflammatory signatures and colonic crypt hyperplasia. Infection also induces dramatic changes to bioenergetics in intestinal epithelial cells, with transition from oxidative phosphorylation (OXPHOS) to aerobic glycolysis and higher abundance of SGLT4, LDHA, and MCT4. Concomitantly, mitochondrial proteins involved in the TCA cycle and OXPHOS were in lower abundance. Similar to observations in C57BL/6 mice, we detected simultaneous activation of cholesterol biogenesis, import, and efflux. Distinctly, however, the pattern recognition receptors NLRP3 and ALPK1 were specifically induced in C3H/HeN. Using cell-based assays revealed that C. rodentium activates the ALPK1/TIFA axis, which is dependent on the ADP-heptose biosynthesis pathway but independent of the Type III secretion system. This study reveals for the first time the unfolding intestinal epithelial cells' responses during severe infectious colitis, which resemble EPEC human infections

Magnetic Connectivity between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation

Extrapolation codes for modelling the magnetic field in the corona in cartesian geometry do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, \textit{e.g.}, a single active region. We apply a method for nonlinear force-free coronal magnetic field modelling of photospheric vector magnetograms in spherical geometry which allows us to study the connectivity between multi-active regions. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic field, where we study three neighbouring magnetically connected active regions (ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between the active regions(ARs). We have studied the time evolution of magnetic field over the period of three days and found no major changes in topologies as there was no major eruption event. From this study we have concluded that active regions are much more connected magnetically than the electric current.Comment: Solar Physic

An E2-ubiquitin thioester-driven approach to identify substrates modified with ubiquitin and ubiquitin-like molecules.

Covalent modifications of proteins with ubiquitin and ubiquitin-like molecules are instrumental to many biological processes. However, identifying the E3 ligase responsible for these modifications remains a major bottleneck in ubiquitin research. Here, we present an E2-thioester-driven identification (E2~dID) method for the targeted identification of substrates of specific E2 and E3 enzyme pairs. E2~dID exploits the central position of E2-conjugating enzymes in the ubiquitination cascade and provides in vitro generated biotinylated E2~ubiquitin thioester conjugates as the sole source for ubiquitination in extracts. This enables purification and mass spectrometry-based identification of modified proteins under stringent conditions independently of the biological source of the extract. We demonstrate the sensitivity and specificity of E2-dID by identifying and validating substrates of APC/C in human cells. Finally, we perform E2~dID with SUMO in S. cerevisiae, showing that this approach can be easily adapted to other ubiquitin-like modifiers and experimental models

Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions

We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and D\'emoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version, having a parabolic current density profile, is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch separatrix surface"-are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-D\'emoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.Comment: 14 pages, 10 figure