Pixelation effects in weak lensing

Weak gravitational lensing can be used to investigate both dark matter and dark energy but requires accurate measurements of the shapes of faint, distant galaxies. Such measurements are hindered by the finite resolution and pixel scale of digital cameras. We investigate the optimum choice of pixel scale for a space-based mission, using the engineering model and survey strategy of the proposed Supernova Acceleration Probe as a baseline. We do this by simulating realistic astronomical images containing a known input shear signal and then attempting to recover the signal using the Rhodes, Refregier, & Groth algorithm. We find that the quality of shear measurement is always improved by smaller pixels. However, in practice, telescopes are usually limited to a finite number of pixels and operational life span, so the total area of a survey increases with pixel size. We therefore fix the survey lifetime and the number of pixels in the focal plane while varying the pixel scale, thereby effectively varying the survey size. In a pure trade-off for image resolution versus survey area, we find that measurements of the matter power spectrum would have minimum statistical error with a pixel scale of 0.09 '' for a 0.14 '' FWHM point-spread function (PSF). The pixel scale could be increased to similar to 0.16 '' if images dithered by exactly half-pixel offsets were always available. Some of our results do depend on our adopted shape measurement method and should be regarded as an upper limit: future pipelines may require smaller pixels to overcome systematic floors not yet accessible, and, in certain circumstances, measuring the shape of the PSF might be more difficult than those of galaxies. However, the relative trends in our analysis are robust, especially those of the surface density of resolved galaxies. Our approach thus provides a snapshot of potential in available technology, and a practical counterpart to analytic studies of pixelation, which necessarily assume an idealized shape measurement method

Strength Tests on Paper Cylinder in Compression, Bending and Shear

Static tests on paper cylinders were conducted at the Langley Memorial Aeronautical Laboratory at Langley Field, Virginia, to obtain qualitative information in connection with a study of the strength of stressed-skin fuselages. The effects of radius-thickness ratio and bulkhead spacing were investigated with the cylinders in compression, bending, combined bending and shear, and torsion

A Comparison of Weak Lensing Measurements From Ground- and Space-Based Facilities

We assess the relative merits of weak lensing surveys, using overlapping imaging data from the ground-based Subaru telescope and the Hubble Space Telescope (HST). Our tests complement similar studies undertaken with simulated data. From observations of 230,000 matched objects in the 2 square degree COSMOS field, we identify the limit at which faint galaxy shapes can be reliably measured from the ground. Our ground-based shear catalog achieves sub-percent calibration bias compared to high resolution space-based data, for galaxies brighter than i'~24.5 and with half-light radii larger than 1.8". This selection corresponds to a surface density of ~15 galaxies per sq arcmin compared to ~71 per sq arcmin from space. On the other hand the survey speed of current ground-based facilities is much faster than that of HST, although this gain is mitigated by the increased depth of space-based imaging desirable for tomographic (3D) analyses. As an independent experiment, we also reconstruct the projected mass distribution in the COSMOS field using both data sets, and compare the derived cluster catalogs with those from X-ray observations. The ground-based catalog achieves a reasonable degree of completeness, with minimal contamination and no detected bias, for massive clusters at redshifts 0.2<z<0.5. The space-based data provide improved precision and a greater sensitivity to clusters of lower mass or at higher redshift.Comment: 12 pages, 8 figures, submitted to ApJ, Higher resolution figures available at http://www.astro.caltech.edu/~mansi/GroundvsSpace.pd

Cheyenne vowel devoicing and transderivational constraints

From the introduction: This brief paper is largely an exercise in lily-gilding, building upon Frantz\u27s insightful analysis of Cheyenne phonology. What I will attempt to do in this paper is to rework some of his rules relating to the devoicing of vowels and raise some questions as to whether these rules confirm the need for a controversial device in the theory of grammar

Operationalising the notion of a restorative school community : a case study in a socio-economically deprived area

In recent years, schools have increasingly begun to opt for an alternative to traditional school punishments: restorative practices. As the practices developed, proponents began to posit that to unlock the true potential of restorative approaches, community involvement was key (this mirrors the opinion of those promoting restorative justice in the criminal system).However, despite this central role for community in the restorative literature, many theorists argue that community involvement is inhibited due to lack of consistent theoretical definition. Additionally, another criticism is that whilst restorative practices are promoted as an effective response to wrongdoing in schools, much of the research has been undertaken in schools where the circumstances are conducive to the deployment of the practices, with amenable staff and a motivated Senior Management Team.My empirical research deviates from these favourable conditions and instead, was undertaken in a school located on one of the most socio-economically deprived estates in the UK. School leaders reported the significant behavioural and social challenges they faced on a consistent basis. Their decision to implement restorative practices was primarily as a salve to mitigate serious challenge and a self-defined chaotic atmosphere brought about by a comprehensive change of management structure and ethos, high rates of staff turnover and historically high levels of violent, prejudicial and dangerous behaviour of students.Through intensive participant and non-participant observation and thirty-three semi- structured interviews with participants involved in all aspects of the school (Senior Management, teachers, students and members of the wider community) my research provides an insight into this school’s use of restorative practices. What emerges from this research is the narrative of a wider community perceived by some participants to be apathetic and disengaged. It exposes the times where the approach of the school and its community contrasts or conflicts and the external factors that impede the school’s ability to utilise restorative approaches. However, this research also indicates the importance of individual relationships of trust between staff and students and how these relationships can exist as a substitute for an absent wider community. It reports the influence and necessity of key school pastoral staff in delivering a small-scale, informal restorative agenda and concludes with the notion that restorative approaches are both feasible and desirable in schools of this type

On the Kernel of the Symbol Map for Multiple Polylogarithms

The symbol map (of Goncharov) takes multiple polylogarithms to a tensor product space where calculations are easier, but where important differential and combinatorial properties of the multiple polylogarithm are retained. Finding linear combinations of multiple polylogarithms in the kernel of the symbol map is an effective way to attempt finding functional equations. We present and utilise methods for finding new linear combinations of multiple polylogarithms (and specifically harmonic polylogarithms) that lie in the kernel of the symbol map. During this process we introduce a new pictorial construction for calculating the symbol, namely the hook-arrow tree, which can be used to easier encode symbol calculations onto a computer. We also show how the hook-arrow tree can simplify symbol calculations where the depth of a multiple polylogarithm is lower than its weight and give explicit expressions for the symbol of depth 2 and 3 multiple polylogarithms of any weight. Using this we give the full symbol for I_{2,2,2}(x,y,z). Through similar methods we also give the full symbol of coloured multiple zeta values. We provide introductory material including the binary tree (of Goncharov) and the polygon dissection (of Gangl, Goncharov and Levin) methods of finding the symbol of a multiple polylogarithm, and give bijections between (adapted forms of) these methods and the hook-arrow tree