Distributed and parallel sparse convex optimization for radio interferometry with PURIFY

Next generation radio interferometric telescopes are entering an era of big data with extremely large data sets. While these telescopes can observe the sky in higher sensitivity and resolution than before, computational challenges in image reconstruction need to be overcome to realize the potential of forthcoming telescopes. New methods in sparse image reconstruction and convex optimization techniques (cf. compressive sensing) have shown to produce higher fidelity reconstructions of simulations and real observations than traditional methods. This article presents distributed and parallel algorithms and implementations to perform sparse image reconstruction, with significant practical considerations that are important for implementing these algorithms for Big Data. We benchmark the algorithms presented, showing that they are considerably faster than their serial equivalents. We then pre-sample gridding kernels to scale the distributed algorithms to larger data sizes, showing application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to 50 billion visibilities, and find that the run-times for the distributed algorithms range from 100 milliseconds to 3 minutes per iteration. This work presents an important step in working towards computationally scalable and efficient algorithms and implementations that are needed to image observations of both extended and compact sources from next generation radio interferometers such as the SKA. The algorithms are implemented in the latest versions of the SOPT (https://github.com/astro-informatics/sopt) and PURIFY (https://github.com/astro-informatics/purify) software packages {(Versions 3.1.0)}, which have been released alongside of this article.Comment: 25 pages, 5 figure

Cost optimization of offshore wind farm combination with reversible solid oxide cell system producing hydrogen using the PyPSA power system modelling tool

In the context of reaching the net zero carbon target, the UK has set an ambitious target of having a green hydrogen production capacity of 5 GW by 2030. As part of the EPSRC-funded project on high efficiency reversible solid oxide cells (rSOC) for the integration of offshore renewable energy (ORE) using hydrogen, eight scenarios where hydrogen is combined with offshore renewable energy were identified. A model using the PyPSA power system modelling tool combined with a sensitivity study, investigated optimized rSOC system capacities, hydrogen storage capacities, and subsea cable connection capacities under various combinations of infrastructure cost, rSOC system efficiencies, and electricity prices for one of the scenarios. Preliminary results for a 600 MW wind farm situated 60 km from shore combined with offshore hydrogen production illustrate the impact of electricity price on decision-making in energy dispatch and on optimization of infrastructure of an ORE-rSOC system. Results indicate that high electricity price fluctuations call for large amounts of hydrogen production and storage capacity. Further refinement of input data would make this approach a promising decision-making tool for the use in the design of an ORE-rSOC system

Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation

We investigate the physics of coherent quantum phase slips in two distinct circuits containing small Josephson junctions: (i) a single junction embedded in an inductive environment and (ii) a long chain of junctions. Starting from the standard Josephson Hamiltonian, the single junction circuit can be analyzed using quasi-classical methods; we formulate the conditions under which the resulting quasi-charge dynamics is exactly dual to the usual phase dynamics associated with Josephson tunneling. For the chain we use the fact that its collective behavior can be characterized by one variable: the number $m$ of quantum phase slips present on it. We conclude that the dynamics of the conjugate quasi-charge is again exactly dual to the standard phase dynamics of a single Josephson junction. In both cases we elucidate the role of the inductance, essential to obtain exact duality. These conclusions have profound consequences for the behavior of single junctions and chains under microwave irradiation. Since both systems are governed by a model exactly dual to the standard resistively and capacitively shunted junction model, we expect the appearance of current-Shapiro steps. We numerically calculate the corresponding current-voltage characteristics in a wide range of parameters. Our results are of interest in view of a metrological current standard

Kerr non-linearity in a superconducting Josephson metamaterial

We present a detailed experimental and theoretical analysis of the dispersion and non-linear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalisation of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find good agreement

Phase-Charge Duality of a Josephson junction in a fluctuating electromagnetic environment

We have measured the current-voltage characteristics of a single Josephson junction placed in a high impedance environment. The transfer of Cooper pairs through the junction is governed by overdamped quasicharge dynamics, leading to Coulomb blockade and Bloch oscillations. Exact duality exists to the standard overdamped phase dynamics of a Josephson junction, resulting in a dual shape of the current-voltage characteristic, with current and voltage changing roles. We demonstrate this duality with experiments which allow for a quantitative comparison with a theory that includes the effect of fluctuations due to finite temperature of the electromagnetic environment

Domino D3.1 - Architecture definition

This deliverable presents the concept of operation of Domino. It includes a description of the systems, subsystems and processes that will be taken into account in the model, as well as the general scope of the model. For each of the mechanisms suggested to be modelled in the project, the deliverable provides a set of possible operational concepts and uptake/scope to be deployed

The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

Objective functions for comparing simulations with insect trap catch data

Targeted surveillance of high risk invasion sites using insect traps is becoming an important tool in border biosecurity, aiding in early detection and subsequent monitoring of eradication attempts. The mark-release-recapture technique is widely used to study the dispersal of insects, and to generate unbiased estimates of population density. It may also be used in the biosecurity context to quantify the efficacy of surveillance and eradication monitoring systems. Marked painted apple moths were released at three different locations in Auckland, New Zealand over six weeks during a recent eradication campaign. The results of the mark-release-recapture experiment were used to parameterise a process-based mechanistic dispersal model in order to understand the moth dispersal pattern in relation to wind patterns, and to provide biosecurity agencies with an ability to predict moth dispersal patterns. A genetic algorithm was used to fit some model parameters. Different objective functions were tested: 1) Cohen’s Kappa test, 2) the sum of squared difference on trap catches, 3) the sum of squared difference weighted by distance from the release site, 4) the sum of squared difference weighted on distance between best-fit paired data. The genetic algorithm proved to be a powerful fitting method, but the model results were highly dependant on the objective function used. Objective functions for fitting spatial data need to characterise spatial patterns as well as density (ie. recapture rate). For fitting stochastic models to datasets derived from stochastic spatial processes, objective functions need to accommodate the fact that a perfect fit is practically impossible, even if the models are the same. Applied on mark-release-recapture data, the Cohen’s Kappa test and the sum of squared difference on trap catches captured respectively the distance component of the spatial pattern and the density component adequately but failed to capture both requirements whereas the sum of squared difference weighted by distance from the release site did. However, in order to integrate the stochastic error generated by the model underlying stochastic process, only the sum of squared difference weighted on distance between best-fit paired data was adequate. The relevance of each of the fitting methods is detailed, and their respective strengths and weaknesses are discussed in relation to their ability to capture the spatial patterns of insect recaptures