Statistical and systematic uncertainties in pixel-based source reconstruction algorithms for gravitational lensing

Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularisation, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid. We also consider regularisation schemes that minimise derivatives of the source (using two finite difference methods) and introduce a scheme that minimises deviations from an analytic source profile. Careful choice of gridding and regularisation can reduce "discreteness noise" in the $\chi^2$ surface that is inherent in the pixel-based methodology. With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realisations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different "observations" can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few percent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves.Comment: 20 pages, 18 figures, accepted to MNRAS, see http://physics.rutgers.edu/~tagoreas/papers/ for high resolution image

Form Accuracy Analysis of Cylindrical Parts Produced by Rapid Prototyping

Solid Freeform fabrication processes are being considered for creating fit and assembly nature functional parts. It is extremely important that these parts are within allowable dimensional and geometric tolerance. The part accuracy produced by rapid prototyping process is greatly affected by the relative orientation of build and face normal directions. A systematic method is needed to find the reliability of the created product. This paper discusses the work done in this area and the effect of build orientation on the part form accuracy analysis of each specified tolerance like circularity and cylindricity. Feasible build direction that can be used to satisfy those tolerances is identified. It will help process engineer in selecting a build direction that can satisfy a mathematical model of form tolerance.Mechanical Engineerin

Support Vector Machine classification of strong gravitational lenses

The imminent advent of very large-scale optical sky surveys, such as Euclid and LSST, makes it important to find efficient ways of discovering rare objects such as strong gravitational lens systems, where a background object is multiply gravitationally imaged by a foreground mass. As well as finding the lens systems, it is important to reject false positives due to intrinsic structure in galaxies, and much work is in progress with machine learning algorithms such as neural networks in order to achieve both these aims. We present and discuss a Support Vector Machine (SVM) algorithm which makes use of a Gabor filterbank in order to provide learning criteria for separation of lenses and non-lenses, and demonstrate using blind challenges that under certain circumstances it is a particularly efficient algorithm for rejecting false positives. We compare the SVM engine with a large-scale human examination of 100000 simulated lenses in a challenge dataset, and also apply the SVM method to survey images from the Kilo-Degree Survey.Comment: Accepted by MNRA

Multi Objective Optimisation of Build Orientation for Rapid Prototyping with Fused Deposition Modeling (FDM)

The ability to select the optimal orientation of build up is one of the critical factors since it affects the part surface quality, accuracy, build time and part cost. Various factors to be considered in optimisation of build orientation for FDM are build material, support material, build up time, surface roughness and total cost. Experiments were carried out and results are analysed for varying build orientation for primitive geometries like cylinder. An appropriate weighting factor has been considered for various objective functions depending on the specific requirement of the part while carrying out multi-objective optimisation. These analyses will help process engineers to decide proper build orientation.Mechanical Engineerin

Origins and Development of Teaching Animal Law in Brazil

This paper examines the strategies utilized on each continent and shows the path made for these scholars to build a framework to discuss animal law within law schools. The conclusion is that this movement produced by such scholars has changed the way law schools are teaching law and is affording new opportunities to solve animal concerns, and likewise, social problems in Brazil and around the world. Therefore, this article first discusses the philosophical Brazilian background to teach animal law, and how the animal rights movement creates a framework for professors and students working in this field. It then summarily explores the Brazilian and United States dialogue and how this partnership has expanded the animal law debate in South America, followed by an examination of the civil law countries that have historically influenced the Brazilian system. That section focuses on Portugal, Spain, and France to define new pedagogy to legal education in Brazil while looking at the Brazilian experience in teaching animal law. Some universities have begun to open discussion and create centers to debate this area. The challenge is to change the way of teaching law by showing students that human and non-human interests need to be considered by the law. Finally, this article proposes a direction and some perspectives for the immediate future and explains that it is time to overcome the obstacles and enjoy the atmosphere already shaped to teach animal law as an autonomous subject, that is, as part of the minimum curriculum in Brazilian law schools

Kabuliwala

A new translation from the Bengali of Rabindranath Tagore's story 'Kabuliwala'

A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074

We present new VLA 22-GHz and e-MERLIN 5-GHz observations of CLASS B1030+074, a two-image strong gravitational lens system whose background source is a compact flat-spectrum radio quasar. In such systems we expect a third image of the background source to form close to the centre of the lensing galaxy. The existence and brightness of such images is important for investigation of the central mass distributions of lensing galaxies, but only one secure detection has been made so far in a galaxy-scale lens system. The noise levels achieved in our new B1030+074 images reach 3 microJy/beam and represent an improvement in central image constraints of nearly an order of magnitude over previous work, with correspondingly better resulting limits on the shape of the central mass profile of the lensing galaxy. Simple models with an isothermal outer power law slope now require either the influence of a central supermassive black hole, or an inner power law slope very close to isothermal, in order to suppress the central image below our detection limit. Using the central mass profiles inferred from light distributions in Virgo galaxies, moved to z=0.5, and matching to the observed Einstein radius, we now find that 45% of such mass profiles should give observable central images, 10% should give central images with a flux density still below our limit, and the remaining systems have extreme demagnification produced by the central SMBH. Further observations of similar objects will therefore allow proper statistical constraints to be placed on the central properties of elliptical galaxies at high redshift.Comment: Accepted by Monthly Notices of the Royal Astronomical Society. 16 pages, 8 figure