Imaging on a Sphere with Interferometers: the Spherical Wave Harmonic Transform

I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is comparable to $w$-term imaging algorithms, but by using a spherical rather than a Cartesian formulation this term has no special significance. The solution presented also allows direct identification of the scalar (spin 0 weighted) spherical harmonics on the sky. The method should be of interest for future multi-spacecraft interferometers, wide-field imaging with non-coplanar arrays, and CMB spherical harmonic measurements using interferometers.Comment: (Fixed references missing in previous arxiv version). This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer revie

A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry

We derive a generalised van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field-of-view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalised vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfilled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional electric field (Jones vector) formalism of the standard "Measurement Equation" of radio astronomical interferometry to the full three-dimensional formalism developed in optical coherence theory. The resulting vC-Z theorem enables all-sky imaging in a single telescope pointing, and imaging using not only standard dual-polarized interferometers (that measure 2-D electric fields), but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2-D Measurement Equation is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We find, however, that such dual-polarized interferometers can have polarimetric aberrations at the edges of the FoV that are often correctable. Our theorem is particularly relevant to proposed and recently developed wide FoV interferometers such as LOFAR and SKA, for which direction-dependent effects will be important.Comment: To be published in MNRA

Sampling errors of correlograms with and without sample mean removal for higher-order complex white noise with arbitrary mean

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean introduces lag dependent covariance between different lags of the correlogram estimates in spite of the lack of covariance in white noise for non-zeros lags. We provide a heuristic rule for when the sample mean should be, and when it should not be, removed if the true mean is not known. The sampling properties derived here are useful is assesing the general statistical performance of autocovariance and autocorrelation estimators in different parameter regimes. Alternatively, the sampling properties could be used as bounds on the detection of a weak signal in general white noise.Comment: 11 pages, 2 figures, To be published in Journal of Time Series Analysi

Managing Research Data: Gravitational Waves

The project which led to this report was funded by JISC in 2010–2011 as part of its ‘Managing Research Data’ programme, to examine the way in which Big Science data is managed, and produce any recommendations which may be appropriate. Big science data is different: it comes in large volumes, and it is shared and exploited in ways which may differ from other disciplines. This project has explored these differences using as a case-study Gravitational Wave data generated by the LSC, and has produced recommendations intended to be useful variously to JISC, the funding council (STFC) and the LSC community. In Sect. 1 we define what we mean by ‘big science’, describe the overall data culture there, laying stress on how it necessarily or contingently differs from other disciplines. In Sect. 2 we discuss the benefits of a formal data-preservation strategy, and the cases for open data and for well-preserved data that follow from that. This leads to our recommendations that, in essence, funders should adopt rather light-touch prescriptions regarding data preservation planning: normal data management practice, in the areas under study, corresponds to notably good practice in most other areas, so that the only change we suggest is to make this planning more formal, which makes it more easily auditable, and more amenable to constructive criticism. In Sect. 3 we briefly discuss the LIGO data management plan, and pull together whatever information is available on the estimation of digital preservation costs. The report is informed, throughout, by the OAIS reference model for an open archive. Some of the report’s findings and conclusions were summarised in [1]. See the document history on page 37

Managing Research Data in Big Science

The project which led to this report was funded by JISC in 2010--2011 as part of its 'Managing Research Data' programme, to examine the way in which Big Science data is managed, and produce any recommendations which may be appropriate. Big science data is different: it comes in large volumes, and it is shared and exploited in ways which may differ from other disciplines. This project has explored these differences using as a case-study Gravitational Wave data generated by the LSC, and has produced recommendations intended to be useful variously to JISC, the funding council (STFC) and the LSC community. In Sect. 1 we define what we mean by 'big science', describe the overall data culture there, laying stress on how it necessarily or contingently differs from other disciplines. In Sect. 2 we discuss the benefits of a formal data-preservation strategy, and the cases for open data and for well-preserved data that follow from that. This leads to our recommendations that, in essence, funders should adopt rather light-touch prescriptions regarding data preservation planning: normal data management practice, in the areas under study, corresponds to notably good practice in most other areas, so that the only change we suggest is to make this planning more formal, which makes it more easily auditable, and more amenable to constructive criticism. In Sect. 3 we briefly discuss the LIGO data management plan, and pull together whatever information is available on the estimation of digital preservation costs. The report is informed, throughout, by the OAIS reference model for an open archive

Deriving the sampling errors of correlograms for general white noise

We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed correlogram, the correlogram with subtracted sample mean, and the fixed-length summation correlogram. For each correlogram we derive explicit formulas for the bias, covariance, mean square error and consistency for generalised higher-order white noise sequences. In particular, this class of sequences may have non-zero means, be complexed valued and also includes non-analytical noise signals. We find that these commonly used correlograms exhibit lag dependent covariance despite the fact that these processes are white and hence by definition do not depend on lag.Comment: Submitted to Biometrik

Sviluppo di una diagnostica per misurare la carica spaziale di un fascio di ioni negativi

Le misure del potenziale di plasma e dello spettro di energia delle particelle secondarie nella regione di deriva di un fascio di ioni negativi danno informazioni sulla formazione di plasma indotta dal fascio e sul trasporto del fascio stesso attraverso gas a bassa pressione. La formazione di plasma in sistemi di fasci di ioni negativi e le caratteristiche di tale plasma sono utili specialmente nell'analisi della compensazione di carica spaziale, che ha un importante impatto sullo studio di fasci di particelle neutre utilizzati per scaldare il plasma all'interno di un tokamak. Dopo una breve introduzione sulle sorgenti di ioni negativi e sulla compensazione di carica spaziale, viene fatta un'analisi dettagliata di quest'ultima. I risultati vengono utilizzati per sviluppare una simulazione numerica e per progettare e costruire una sonda a potenziale ritardante per lo studio della compensazione di carica spaziale. Dopo la costruzione, la sonda viene testata in un dispositivo magnetron per sputtering. I risultati del test sono ottimi: molto insegnano sul funzionamento della sonda e inoltre suggeriscono come continuare il lavoro futuro.ope

Brexit and the location of migrants

Posted by Felipe Carozzi, SERC & LSE The results of the recent vote to leave the EU have come with a plethora of cross-sectional and spatial analyses, provided by the different British media outlets and their data journalists since Friday morning. We have learned about the generational profile of voters, the poor results of the stay campaign on traditional labour strongholds, the wide difference between results in large cities and small towns. While it is often hard to give a clear interpretation to these correlations, it is natural that we build our narratives and explanations of what happened on Friday with these elements