1,682 research outputs found

    Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

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    In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequencyComment: 6 figures, 13 page

    UAV photogrammetry and structure from motion to assess calving dynamics at Store Glacier, a large outlet draining the Greenland ice sheet

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    This study presents the application of a cost-effective, unmanned aerial vehicle (UAV) to investigate calving dynamics at a major marine-terminating outlet glacier draining the western sector of the Greenland ice sheet. The UAV was flown over Store Glacier on three sorties during summer 2013 and acquired over 2000 overlapping, geotagged images of the calving front at an ~40 cm ground sampling distance. Stereo-photogrammetry applied to these images enabled the extraction of high-resolution digital elevation models (DEMs) with vertical accuracies of ± 1.9 m which were used to quantify glaciological processes from early July to late August 2013. The central zone of the calving front advanced by ~500 m, whilst the lateral margins remained stable. The orientation of crevasses and the surface velocity field derived from feature tracking indicates that lateral drag is the primary resistive force and that ice flow varies across the calving front from 2.5 m d−1 at the margins to in excess of 16 m d−1 at the centreline. Ice flux through the calving front is 3.8 × 107 m3 d−1, equivalent to 13.9 Gt a−1 and comparable to flux-gate estimates of Store Glacier's annual discharge. Water-filled crevasses were present throughout the observation period but covered a limited area of between 0.025 and 0.24% of the terminus and did not appear to exert any significant control over fracture or calving. We conclude that the use of repeat UAV surveys coupled with the processing techniques outlined in this paper have great potential for elucidating the complex frontal dynamics that characterise large calving outlet glaciers

    Stochastic simulations of conditional states of partially observed systems, quantum and classical

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    In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix ρr(t)\rho_r(t) and if classical the conditional state will be given by a probability distribution Pr(x,t)P_r(x,t) where rr is the result of the measurement. Thus to determine the evolution of this conditional state under continuous-in-time monitoring requires an expensive numerical calculation. In this paper we demonstrating a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of NN, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure

    The Distribution of Redshifts in New Samples of Quasi-stellar Objects

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    Two new samples of QSOs have been constructed from recent surveys to test the hypothesis that the redshift distribution of bright QSOs is periodic in log(1+z)\log(1+z). The first of these comprises 57 different redshifts among all known close pairs or multiple QSOs, with image separations \leq 10\arcsec, and the second consists of 39 QSOs selected through their X-ray emission and their proximity to bright comparatively nearby active galaxies. The redshift distributions of the samples are found to exhibit distinct peaks with a periodic separation of 0.089\sim 0.089 in log(1+z)\log(1+z) identical to that claimed in earlier samples but now extended out to higher redshift peaks z=2.63,3.45z = 2.63, 3.45 and 4.47, predicted by the formula but never seen before. The periodicity is also seen in a third sample, the 78 QSOs of the 3C and 3CR catalogues. It is present in these three datasets at an overall significance level 10510^{-5} - 10610^{-6}, and appears not to be explicable by spectroscopic or similar selection effects. Possible interpretations are briefly discussed.Comment: submitted for publication in the Astronomical Journal, 15 figure

    The Performance of Private Equity Funds: Does Diversification Matter?

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    This paper is the first systematic analysis of the impact of diversification on the performance of private equity funds. A unique data set allows the exact evaluation of diversification across the dimensions financing stages, industries, and countries. Very different levels of diversification can be observed across sample funds. While some funds are highly specialized others are highly diversified. The empirical results show that the rate of return of private equity funds declines with diversification across financing stages, but increases with diversification across industries. Accordingly, the fraction of portfolio companies which have a negative return or return nothing at all, increase with diversification across financing stages. Diversification across countries has no systematic effect on the performance of private equity funds
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