Bayesian T-optimal discriminating designs

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the T-optimality criterion introduced by Atkinson and Fedorov (1975a) is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally T-optimal discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. A new efficient method is developed to deal with problems of this type. It combines some features of the classical exchange type algorithm with the gradient methods. Convergence is proved and it is demonstrated that the new method can find Bayesian optimal discriminating designs in situations where all currently available procedures fail.Comment: 25 pages, 3 figure

The finite mass beamsplitter in high power interferometers

The beamplitter in high-power interferometers is subject to significant radiation-pressure fluctuations. As a consequence, the phase relations which appear in the beamsplitter coupling equations oscillate and phase modulation fields are generated which add to the reflected fields. In this paper, the transfer function of the various input fields impinging on the beamsplitter from all four ports onto the output field is presented including radiation-pressure effects. We apply the general solution of the coupling equations to evaluate the input-output relations of the dual-recycled laser-interferometer topology of the gravitational-wave detector GEO600 and the power-recycling, signal-extraction topology of advanced LIGO. We show that the input-output relation exhibits a bright-port dark-port coupling. This mechanism is responsible for bright-port contributions to the noise density of the output field and technical laser noise is expected to decrease the interferometer's sensitivity at low frequencies. It is shown quantitatively that the issue of technical laser noise is unimportant in this context if the interferometer contains arm cavities.Comment: 10 pages, 7 figure

Detection of Majorana Kramers pairs using a quantum point contact

We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of $\pi$ across the Josephson junction. We investigate the detection of these Majorana pairs with the integrated QPC, and find a robust switching from normal to Andreev scattering across the edges due to the presence of Majorana Kramers pairs. This transport signature is expected to be exhibited in measurements of differential conductance and/or current cross-correlation at low bias

The location, clustering, and propagation of massive star formation in giant molecular clouds

Massive stars are key players in the evolution of galaxies, yet their formation pathway remains unclear. In this work, we use data from several galaxy-wide surveys to build an unbiased dataset of ~700 massive young stellar objects (MYSOs), ~200 giant molecular clouds (GMCs), and ~100 young (<10 Myr) optical stellar clusters (SCs) in the Large Magellanic Cloud. We employ this data to quantitatively study the location and clustering of massive star formation and its relation to the internal structure of GMCs. We reveal that massive stars do not typically form at the highest column densities nor centers of their parent GMCs at the ~6 pc resolution of our observations. Massive star formation clusters over multiple generations and on size scales much smaller than the size of the parent GMC. We find that massive star formation is significantly boosted in clouds near SCs. Yet, whether a cloud is associated with a SC does not depend on either the cloud's mass or global surface density. These results reveal a connection between different generations of massive stars on timescales up to 10 Myr. We compare our work with Galactic studies and discuss our findings in terms of GMC collapse, triggered star formation, and a potential dichotomy between low- and high-mass star formation.Comment: 13 pages, 7 figures, in pres