Modal decomposition of astronomical images with application to shapelets

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis functions, which may be linearly dependent, non-orthogonal and incomplete. It is shown that such circumstances may result even from the digitisation of continuous basis functions that are orthogonal and complete. In particular, digitised shapelet basis functions are investigated and are shown to suffer from such difficulties. As a result the standard method of performing shapelet analysis produces unnecessarily inaccurate decompositions. The optimal method presented here is shown to yield more accurate decompositions in all cases.Comment: 12 pages, 17 figures, submitted to MNRA

Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

In-service Initial Teacher Education in the Learning and Skills Sector in England: Integrating Course and Workplace Learning

The aim of the paper is to advance understanding of in-service learning and skills sector trainee teachers’ learning and propose ways of improving their learning. A conceptual framework is developed by extending Billett’s (International Journal of Educational Research 47:232–240, 2008) conceptualisation of workplace learning, as a relationally interdependent process between the opportunities workplaces afford for activities and interactions and how individuals engage with these, to a third base of participation, the affordances of the initial teacher education course. Hager and Hodkinson’s (British Educational Research Journal 35:619–638, 2009) metaphor of ‘learning as becoming’ is used to conceptualise the ways trainees reconstruct learning in a continuous transactional process of boundary crossing between course and workplace. The findings of six longitudinal case studies of trainees’ development, and evidence from other studies, illustrate the complex interrelationships between LSS workplace affordances, course affordances and trainee characteristics and the ways in which trainees reconstruct learning in each setting. The experience of teaching and interacting with learners, interactions with colleagues, and access to workplace resources and training are important workplace affordances for learning. However, some trainees have limited access to these affordances. Teaching observations, course activities and experiences as a learner are significant course affordances. Trainees’ beliefs, prior experiences and dispositions vary and significantly influence their engagement with course and workplace affordances. It is proposed that better integration of course and workplace learning through guided participation in an intentional workplace curriculum and attention to the ways trainees choose to engage with this, together with the use of practical theorising has the potential to improve trainee learning

Scale-invariant gauge theories of gravity: Theoretical foundations

We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincaré invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations, which allow for a more transparent interpretation of such theories in terms of gauge fields in Minkowski spacetime. Our approach therefore differs from the usual geometrical description of locally scale-invariant Poincaré gauge theory (PGT) and Weyl gauge theory (WGT) in terms of Riemann–Cartan and Weyl–Cartan spacetimes, respectively. In particular, we reconsider the interpretation of the Einstein gauge and also the equations of motion of matter fields and test particles in these theories. Inspired by the observation that the PGT and WGT matter actions for the Dirac field and electromagnetic field have more general invariance properties than those imposed by construction, we go on to present a novel alternative to WGT by considering an “extended” form for the transformation law of the rotational gauge field under local dilations, which includes its “normal” transformation law in WGT as a special case. The resulting “extended” Weyl gauge theory (eWGT) has a number of interesting features that we describe in detail. In particular, we present a new scale-invariant gauge theory of gravity that accommodates ordinary matter and is defined by the most general parity-invariant eWGT Lagrangian that is at most quadratic in the eWGT field strengths, and we derive its field equations. We also consider the construction of PGTs that are invariant under local dilations assuming either the “normal” or “extended” transformation law for the rotational gauge field, but show that they are special cases of WGT and eWGT, respectively.This is the final version of the article. It first appeared from the American Institute of Physics via http://dx.doi.org/10.1063/1.496314

Alternative Fourier Expansions for Inverse Square Law Forces

Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an alternative based on a compact, cylindrical Green's function expansion that should have wide applicability throughout physics. Two-electron "direct" and "exchange" integrals in many-electron quantum systems are evaluated to illustrate the procedure which is more compact than the standard one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure

Scalability tests of R-GMA-based grid job monitoring system for CMS Monte Carlo data production

Copyright @ 2004 IEEEHigh-energy physics experiments, such as the compact muon solenoid (CMS) at the large hadron collider (LHC), have large-scale data processing computing requirements. The grid has been chosen as the solution. One important challenge when using the grid for large-scale data processing is the ability to monitor the large numbers of jobs that are being executed simultaneously at multiple remote sites. The relational grid monitoring architecture (R-GMA) is a monitoring and information management service for distributed resources based on the GMA of the Global Grid Forum. We report on the first measurements of R-GMA as part of a monitoring architecture to be used for batch submission of multiple Monte Carlo simulation jobs running on a CMS-specific LHC computing grid test bed. Monitoring information was transferred in real time from remote execution nodes back to the submitting host and stored in a database. In scalability tests, the job submission rates supported by successive releases of R-GMA improved significantly, approaching that expected in full-scale production

Bayesian model comparison applied to the Explorer-Nautilus 2001 coincidence data

Bayesian reasoning is applied to the data by the ROG Collaboration, in which gravitational wave (g.w.) signals are searched for in a coincidence experiment between Explorer and Nautilus. The use of Bayesian reasoning allows, under well defined hypotheses, even tiny pieces of evidence in favor of each model to be extracted from the data. The combination of the data of several experiments can therefore be performed in an optimal and efficient way. Some models for Galactic sources are considered and, within each model, the experimental result is summarized with the likelihood rescaled to the insensitivity limit value (``${\cal R}$ function''). The model comparison result is given in in terms of Bayes factors, which quantify how the ratio of beliefs about two alternative models are modified by the experimental observationComment: 16 pages, 4 figures. Presented at the GWDAW2002 conference, held in Kyoto on Dec.,2002. This version includes comments by the referees of CQG, which has accepted the paper for pubblication in the special issue of the conference. In particular, note that in Eq. 12 there was a typeset error. As suggested by one of the referees, a uniform prior in Log(alpha) has also been considere

The Quantum-Classical Correspondence in Polygonal Billiards

We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly related to the classical invariant surfaces in the semiclassical limit. This is illustrated for the barrier billiard. We expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines.Comment: 8 pages, 9 figures (in reduced quality), to appear in PR

Measuring AGN Feedback with the Sunyaev-Zel'dovich Effect

One of the most important and poorly-understood issues in structure formation is the role of outflows driven by active galactic nuclei (AGN). Using large-scale cosmological simulations, we compute the impact of such outflows on the small-scale distribution of the cosmic microwave background (CMB). Like gravitationally-heated structures, AGN outflows induce CMB distortions both through thermal motions and peculiar velocities, by processes known as the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects, respectively. For AGN outflows the thermal SZ effect is dominant, doubling the angular power spectrum on arcminute scales. But the most distinct imprint of AGN feedback is a substantial increase in the thermal SZ distortions around elliptical galaxies, post-starburst ellipticals, and quasars, which is linearly proportional to the outflow energy. While point source subtraction is difficult for quasars, we show that by appropriately stacking microwave measurements around early-type galaxies, the new generation of small-scale microwave telescopes will be able to directly measure AGN feedback at the level important for current theoretical models.Comment: 12 pages, 12 figures, submitted to ApJ (comments welcome