7,657 research outputs found
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 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 -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 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
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