Excursion to Sandgate and Folkestone

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Strongly quadrature-dependent noise in superconducting micro-resonators measured at the vacuum-noise limit

We measure frequency- and dissipation-quadrature noise in superconducting lithographed microwave resonators with sensitivity near the vacuum noise level using a Josephson parametric amplifier. At an excitation power of 100~nW, these resonators show significant frequency noise caused by two-level systems. No excess dissipation-quadrature noise (above the vacuum noise) is observed to our measurement sensitivity. These measurements demonstrate that the excess dissipation-quadrature noise is negligible compared to vacuum fluctuations, at typical readout powers used in micro-resonator applications. Our results have important implications for resonant readout of various devices such as detectors, qubits and nano-mechanical oscillators.Comment: 13 pages, 4 figure

Data compression in the presence of observational error correlations

Numerical weather prediction (NWP) models are moving towards km-scale (and smaller) resolutions in order to forecast high-impact weather. As the resolution of NWP models increase the need for high-resolution observations to constrain these models also increases. A major hurdle to the assimilation of dense observations in NWP is the presence of non-negligible observation error correlations (OECs). Despite the difficulty in estimating these error correlations, progress is being made, with centres around the world now explicitly accounting for OECs in a variety of observation types. This paper explores how to make efficient use of this potentially dramatic increase in the amount of data available for assimilation. In an idealised framework it is illustrated that as the length-scales of the OECs increase the scales that the analysis is most sensitive to the observations become smaller. This implies that a denser network of observations is more beneficial with increasing OEC length-scales. However, the computational and storage burden associated with such a dense network may not be feasible. To reduce the amount of data, a compression technique based on retaining the maximum information content of the observations can be used. When the OEC length-scales are large (in comparison to the prior error correlations), the data compression will select observations of the smaller scales for assimilation whilst throwing out the larger scale information. In this case it is shown that there is a discrepancy between the observations with the maximum information and those that minimise the analysis error variances. Experiments are performed using the Ensemble Kalman Filter and the Lorenz-1996 model, comparing different forms of data reduction. It is found that as the OEC length-scales increase the assimilation becomes more sensitive to the choice of data reduction technique

Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame cases. The algebra of row-column-finite (or locally finite) matrices over an arbitrary field is one of the algebras considered in this paper, its representation type is shown to be finite.Comment: 33 page