Type Ia Supernova Intrinsic Magnitude Dispersion and the Fitting of Cosmological Parameters

I present an analysis for fitting cosmological parameters from a Hubble Diagram of a standard candle with unknown intrinsic magnitude dispersion. The dispersion is determined from the data themselves, simultaneously with the cosmological parameters. This contrasts with the strategies used to date. The advantages of the presented analysis are that it is done in a single fit (it is not iterative), it provides a statistically founded and unbiased estimate of the intrinsic dispersion, and its cosmological-parameter uncertainties account for the intrinsic dispersion uncertainty. Applied to Type Ia supernovae, my strategy provides a statistical measure to test for sub-types and assess the significance of any magnitude corrections applied to the calibrated candle. Parameter bias and differences between likelihood distributions produced by the presented and currently-used fitters are negligibly small for existing and projected supernova data sets.Comment: 15 pages, 6 figures, accepted by the Publications of the Astronomical Society of the Pacifi

Dithering Strategies and Point-Source Photometry

The accuracy in the photometry of a point source depends on the point-spread function (PSF), detector pixelization, and observing strategy. The PSF and pixel response describe the spatial blurring of the source, the pixel scale describes the spatial sampling of a single exposure, and the observing strategy determines the set of dithered exposures with pointing offsets from which the source flux is inferred. In a wide-field imaging survey, sources of interest are randomly distributed within the field of view and hence are centered randomly within a pixel. A given hardware configuration and observing strategy therefore have a distribution of photometric uncertainty for sources of fixed flux that fall in the field. In this article we explore the ensemble behavior of photometric and position accuracies for different PSFs, pixel scales, and dithering patterns. We find that the average uncertainty in the flux determination depends slightly on dither strategy, whereas the position determination can be strongly dependent on the dithering. For cases with pixels much larger than the PSF, the uncertainty distributions can be non-Gaussian, with rms values that are particularly sensitive to the dither strategy. We also find that for these configurations with large pixels, pointings dithered by a fractional pixel amount do not always give minimal average uncertainties; this is in contrast to image reconstruction for which fractional dithers are optimal. When fractional pixel dithering is favored, a pointing accuracy of better than $\sim 0.15$ pixel width is required to maintain half the advantage over random dithers

The Efficiency of Decentralised and Devolved Government: A Framework

A wide range of geographically decentralised governance structures exists across countries (Ter-Minassian, 1997). These differences in administrative and constitutional mechanisms come about, at least partly, by historical accident and wider political factors. However, in this paper we focus on the more narrowly defined efficiency implications of such arrangements. This is useful for identifying the motives that might underlie particular administrative set ups and the possible efficiency losses associated with specific forms of decentralisation or devolution. In particular, we develop a framework that allows a comparison of the effectiveness of implementing policy through three alternative systems. These are: a centralised; a decentralised; and a fully devolved structure. In this analysis we build on the work of Canes-Wrone et al, (2001) and Maskin and Tirole (2004) on representative democracy. The novelty is that we place this analysis in the context of a potentially decentralised or devolved regional administration. We find that the choice of appropriate administrative form depends upon the degree of homogeneity between regions, the relative efficiency of regional decision makers and their time discount rate.

Topological superconductivity in ferromagnetic atom chains beyond the deep-impurity regime

Recent developments in the search for topological superconductivity have brought lattices of magnetic adatoms on a superconductor into intense focus. In this work we will study ferromagnetic chains of adatoms on superconducting surfaces with Rashba spin-orbit coupling. Generalising the deep-impurity approach employed extensively in previous works to arbitrary subgap energies, we formulate the theory of the subgap spectrum as a nonlinear matrix eigenvalue problem. We obtain an essentially analytical description of the subgap spectrum, allowing an efficient study of the topological properties. Employing a flat-band Hamiltonian sharing the topological properties of the chain, we evaluate the $\mathbb{Z}$-valued winding number and discover five distinct topological phases. Our results also confirm that the topological band formation does not require the decoupled Shiba energies to be fine-tuned to the gap centre. We also study the properties of Majorana bound states in the system.Comment: 11 pages, 16 figure

Majorana states in helical Shiba chains and ladders

Motivated by recent proposals to realize Majorana bound states in chains and arrays of magnetic atoms deposited on top of a superconductor, we study the topological properties of various chain structures, ladders and two-dimensional arrangements exhibiting magnetic helices. We show that magnetic domain walls where the chirality of a magnetic helix is inverted support two protected Majorana states giving rise to a tunneling conductance peak twice the height of a single Majorana state. The topological properties of coupled chains exhibit nontrivial behaviour as a function of the number of chains beyond the even-odd dichotomy expected from the simple $\mathbb{Z}_2$ nature of coupled Majorana states. In addition, it is possible that a ladder of two or more coupled chains exhibit Majorana edge states even when decoupled chains are trivial. We formulate a general criterion for the number of Majorana edge states in multichain ladders and discuss some experimental consequences of our findings.Comment: 6 pages, 7 Fig