Emulating computer models with step-discontinuous outputs using Gaussian processes

In many real-world applications, we are interested in approximating functions that are analytically unknown. An emulator provides a "fast" approximation of such functions relying on a limited number of evaluations. Gaussian processes (GPs) are commonplace emulators due to their properties such as the ability to quantify uncertainty. GPs are essentially developed to emulate smooth, continuous functions. However, the assumptions of continuity and smoothness is unwarranted in many situations. For example, in computer models where bifurcation, tipping points occur in their systems of equations, the outputs can be discontinuous. This paper examines the capacity of GPs for emulating step-discontinuous functions using two approaches. The first approach is based on choosing covariance functions/kernels, namely neural network and Gibbs, that are most appropriate for modelling discontinuities. The predictive performance of these two kernels is illustrated using several examples. The results show that they have superior performance to standard covariance functions, such as the Mat\'ern family, in capturing sharp jumps. The second approach is to transform the input space such that in the new space a GP with a standard kernel is able to predict the function well. A parametric transformation function is used whose parameters are estimated by maximum likelihood.Engineering and Physical Sciences Research Council (EPSRC

Non-Gaussian Radio-Wave Scattering in the Interstellar Medium

It was recently suggested by Boldyrev & Gwinn that the characteristics of radio scintillations from distant pulsars are best understood if the interstellar electron-density fluctuations that cause the time broadening of the radio pulses obey non-Gaussian statistics. In this picture the density fluctuations are inferred to be strong on very small scales ($\sim 10^8-10^{10} {cm}$). We argue that such density structures could correspond to the ionized boundaries of molecular regions (clouds) and demonstrate that the power-law distribution of scattering angles that is required to match the observations arises naturally from the expected intersections of our line of sight with randomly distributed, thin, approximately spherical ionized shells of this type. We show that the observed change in the time-broadening behavior for pulsar dispersion measures $\lesssim 30 {\rm pc} {\rm cm}^{-3}$ is consistent with the expected effect of the general ISM turbulence, which should dominate the scattering for nearby pulsars. We also point out that if the clouds are ionized by nearby stars, then their boundaries may become turbulent on account of an ionization front instability. This turbulence could be an alternative cause of the inferred density structures. An additional effect that might contribute to the strength of the small-scale fluctuations in this case is the expected flattening of the turbulent density spectrum when the eddy sizes approach the proton gyroscale.Comment: 15 pages, 3 figures, accepted to Ap

Planetary systems around close binary stars: the case of the very dusty, Sun-like, spectroscopic binary BD+20 307

Field star BD+20 307 is the dustiest known main sequence star, based on the fraction of its bolometric luminosity, 4%, that is emitted at infrared wavelengths. The particles that carry this large IR luminosity are unusually warm, comparable to the temperature of the zodiacal dust in the solar system, and their existence is likely to be a consequence of a fairly recent collision of large objects such as planets or planetary embryos. Thus, the age of BD+20 307 is potentially of interest in constraining the era of terrestrial planet formation. The present project was initiated with an attempt to derive this age using the Chandra X-ray Observatory to measure the X-ray flux of BD+20 307 in conjunction with extensive photometric and spectroscopic monitoring observations from Fairborn Observatory. However, the recent realization that BD+20 307 is a short period, double-line, spectroscopic binary whose components have very different lithium abundances, vitiates standard methods of age determination. We find the system to be metal-poor; this, combined with its measured lithium abundances, indicates that BD+20 307 may be several to many Gyr old. BD+20 307 affords astronomy a rare peek into a mature planetary system in orbit around a close binary star (because such systems are not amenable to study by the precision radial velocity technique).Comment: accepted for ApJ, December 10, 200

Continuous cough monitoring using ambient sound recording during convalescence from a COPD exacerbation

Purpose Cough is common in chronic obstructive pulmonary disease (COPD) and is associated with frequent exacerbations and increased mortality. Cough increases during acute exacerbations (AE-COPD), representing a possible metric of clinical deterioration. Conventional cough monitors accurately report cough counts over short time periods. We describe a novel monitoring system which we used to record cough continuously for up to 45 days during AE-COPD convalescence. Methods This is a longitudinal, observational study of cough monitoring in AE-COPD patients discharged from a single teaching-hospital. Ambient sound was recorded from two sites in the domestic environment and analysed using novel cough classifier software. For comparison, the validated hybrid HACC/LCM cough monitoring system was used on days 1, 5, 20 and 45. Patients were asked to record symptoms daily using diaries. Results Cough monitoring data were available for 16 subjects with a total of 568 monitored days. Daily cough count fell significantly from mean±SEM 272.7±54.5 on day 1 to 110.9±26.3 on day 9 (p<0.01) before plateauing. The absolute cough count detected by the continuous monitoring system was significantly lower than detected by the hybrid HACC/LCM system but normalised counts strongly correlated (r=0.88, p<0.01) demonstrating an ability to detect trends. Objective cough count and subjective cough scores modestly correlated (r=0.46). Conclusions Cough frequency declines significantly following AE-COPD and the reducing trend can be detected using continuous ambient sound recording and novel cough classifier software. Objective measurement of cough frequency has the potential to enhance our ability to monitor the clinical state in patients with COPD

Attitude-referenced radiometer study. Volume 2 - Precision radiometric system

Attitude reference radiometer study for earth orbiting spacecraf

Theoretical interpretation of the experimental electronic structure of lens shaped, self-assembled InAs/GaAs quantum dots

We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens shaped InAs quantum dots within the ``linear combination of bulk bands'' method. We present a detailed comparison with experiment, including quantites such as the single particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole and electron hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.Comment: 16 pages, 5 figures. Submitted to Physical Review

Variational quantum Monte Carlo calculations for solid surfaces

Quantum Monte Carlo methods have proven to predict atomic and bulk properties of light and non-light elements with high accuracy. Here we report on the first variational quantum Monte Carlo (VMC) calculations for solid surfaces. Taking the boundary condition for the simulation from a finite layer geometry, the Hamiltonian, including a nonlocal pseudopotential, is cast in a layer resolved form and evaluated with a two-dimensional Ewald summation technique. The exact cancellation of all Jellium contributions to the Hamiltonian is ensured. The many-body trial wave function consists of a Slater determinant with parameterized localized orbitals and a Jastrow factor with a common two-body term plus a new confinement term representing further variational freedom to take into account the existence of the surface. We present results for the ideal (110) surface of Galliumarsenide for different system sizes. With the optimized trial wave function, we determine some properties related to a solid surface to illustrate that VMC techniques provide standard results under full inclusion of many-body effects at solid surfaces.Comment: 9 pages with 2 figures (eps) included, Latex 2.09, uses REVTEX style, submitted to Phys. Rev.