Bayesian Optimal Design for Ordinary Differential Equation Models

Bayesian optimal design is considered for experiments where it is hypothesised that the responses are described by the intractable solution to a system of non-linear ordinary differential equations (ODEs). Bayesian optimal design is based on the minimisation of an expected loss function where the expectation is with respect to all unknown quantities (responses and parameters). This expectation is typically intractable even for simple models before even considering the intractability of the ODE solution. New methodology is developed for this problem that involves minimising a smoothed stochastic approximation to the expected loss and using a state-of-the-art stochastic solution to the ODEs, by treating the ODE solution as an unknown quantity. The methodology is demonstrated on three illustrative examples and a real application involving estimating the properties of human placentas

General aviation approach and landing practices

The characteristics of air traffic patterns at uncontrolled airports and techniques used by a group of general aviation pilots in landing light airplanes are documented. The results of some 1,600 radar tracks taken at four uncontrolled airports and some 600 landings made by 22 pilots in two, four place, single engine light airplanes show that the uncontrolled traffic pattern is highly variable. The altitudes, distances, and piloting procedures utilized may affect the ability for pilots to see-and-avoid in this environment. Most landing approaches were conducted at an airspeed above recommended, resulting in significant floating during flare and touchdowns that were relatively flat and often nose-low

PCA of PCA: Principal Component Analysis of Partial Covering Absorption in NGC 1365

We analyse 400 ks of XMM-Newton data on the active galactic nucleus NGC 1365 using principal component analysis (PCA) to identify model independent spectral components. We find two significant components and demonstrate that they are qualitatively different from those found in MCG?6-30-15 using the same method. As the variability in NGC 1365 is known to be due to changes in the parameters of a partial covering neutral absorber, this shows that the same mechanism cannot be the driver of variability in MCG-6-30-15. By examining intervals where the spectrum shows relatively low absorption we separate the effects of intrinsic source variability, including signatures of relativistic reflection, from variations in the intervening absorption. We simulate the principal components produced by different physical variations, and show that PCA provides a clear distinction between absorption and reflection as the drivers of variability in AGN spectra. The simulations are shown to reproduce the PCA spectra of both NGC 1365 and MCG-6-30-15, and further demonstrate that the dominant cause of spectral variability in these two sources requires a qualitatively different mechanism.Comment: 8 pages, 10 figures. Accepted for publication in MNRA

Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate

We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the non-adiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyse the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.Comment: In this version (the published version) we have slightly rewritten the manuscript in places and have corrected some typos. 15 pages and 13 figure

Properties of AGN coronae in the NuSTAR era

The focussing optics of NuSTAR have enabled high signal-to-noise spectra to be obtained from many X-ray bright Active Galactic Nuclei (AGN) and Galactic Black Hole Binaries (BHB). Spectral modelling then allows robust characterization of the spectral index and upper energy cutoff of the coronal power-law continuum, after accounting for reflection and absorption effects. Spectral-timing studies, such as reverberation and broad iron line fitting, of these sources yield coronal sizes, often showing them to be small and in the range of 3 to 10 gravitational radii in size. Our results indicate that coronae are hot and radiatively compact, lying close to the boundary of the region in the compactness - temperature diagram which is forbidden due to runaway pair production. The coincidence suggests that pair production and annihilation are essential ingredients in the coronae of AGN and BHB and that they control the shape of the observed spectra.Comment: 11 pages, 8 figures, accepted for publication in MNRA