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Register a new userThe non-coplanar baselines effect in radio interferometry: The W-Projection algorithm
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We consider a troublesome form of non-isoplanatism in synthesis radio telescopes: non-coplanar baselines. We present a novel interpretation of the non-coplanar baselines effect as being due to differential Fresnel diffraction in the neighborhood of the array antennas. We have developed a new algorithm to deal with this effect. Our new algorithm, which we call W-projection, has markedly superior performance compared to existing algorithms. At roughly equivalent levels of accuracy, W-projection can be up to an order of magnitude faster than the corresponding facet-based algorithms. Furthermore, the precision of result is not tightly coupled to computing time. W-projection has important consequences for the design and operation of the new generation of radio telescopes operating at centimeter and longer wavelengths.
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Next-generation radio interferometric telescopes will exhibit non-coplanar baseline configurations and wide field-of-views, inducing a w-modulation of the sky image, which in turn induces the spread spectrum effect. We revisit the impact of this effect on imaging quality and study a new algorithmic strategy to deal with the associated operator in the image reconstruction process. In previous studies it has been shown that image recovery in the framework of compressed sensing is improved due to the spread spectrum effect, where the w-modulation can act to increase the incoherence between measurement and sparsifying signal representations. For the purpose of computational efficiency, idealised experiments were performed, where only a constant baseline component w in the pointing direction of the telescope was considered. We extend this analysis to the more realistic setting where the w-component varies for each visibility measurement. Firstly, incorporating varying w-components into imaging algorithms is a computational demanding task. We propose a variant of the w-projection algorithm for this purpose, which is based on an adaptive sparsification procedure, and incorporate it in compressed sensing imaging methods. This sparse matrix variant of the w-projection algorithm is generic and adapts to the support of each kernel. Consequently, it is applicable for all types of direction-dependent effects. Secondly, we show that for w-modulation with varying w-components, reconstruction quality is significantly improved compared to the setting where there is no w-modulation (i.e. w=0), reaching levels comparable to the quality of a constant, maximal w-component. This finding confirms that one may seek to optimise future telescope configurations to promote large w-components, thus enhancing the spread spectrum effect and consequently the fidelity of image reconstruction.
We study the impact of the spread spectrum effect in radio interferometry on the quality of image reconstruction. This spread spectrum effect will be induced by the wide field-of-view of forthcoming radio interferometric telescopes. The resulting chirp modulation improves the quality of reconstructed interferometric images by increasing the incoherence of the measurement and sparsity dictionaries. We extend previous studies of this effect to consider the more realistic setting where the chirp modulation varies for each visibility measurement made by the telescope. In these first preliminary results, we show that for this setting the quality of reconstruction improves significantly over the case without chirp modulation and achieves almost the reconstruction quality of the case of maximal, constant chirp modulation.
We present a novel and simple algorithm in the variation after projection (VAP) approach for the non-yrast nuclear states. It is for the first time that the yrast state and non-yrast states can be varied on the same footing. The orthogonality among the calculated states is automatically fulfilled by solving the Hill-Wheeler equation. This avoids the complexity of the frequently used Gram-Schmidt orthogonalization, as adopted by the excited VAMPIR method. Thanks to the Cauchys interlacing theorem in the matrix theory, the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. Once such minimization is converged, all the calculated energies and the corresponding states can be obtained, simultaneously. The present VAP calculations are performed with time-odd Hartree-Fock Slater determinants. It is shown that the calculated VAP energies (both yrast and non-yrast) are very close to the corresponding ones from the full shell model calculations. It looks the present algorithm is not limited to the VAP, but should be universal, i.e., one can do the variation with different forms of the many-body wavefunctions to calculate the excited states in different quantum many-body systems.
The topological Hall effect (THE), induced by the Berry curvature, which originates from non-zero scalar spin chirality, is an important feature for mesoscopic topological structures, such as skyrmions. However, the THE might also arise from other microscopic non-coplanar spin structures in the lattice. Thus, the origin of the THE inevitably needs to be determined to fully understand skyrmions and find new host materials. Here, we examine the Hall effect in both bulk- and micron-sized lamellar samples of MnBi. The sample size affects the temperature and field range in which the THE is detectable. Although bulk sample exhibits the THE only upon exposure to weak fields in the easy-cone state, in thin lamella the THE exists across a wide temperature range and occurs at fields near saturation. Our results show that both the non-coplanar spin structure in the lattice and topologically non-trivial skyrmion bubbles are responsible for the THE, and that the dominant mechanism depends on the sample size. Hence, the magnetic phase diagram for MnBi is strongly size-dependent. Our study provides an example in which the THE is simultaneously induced by two mechanisms, and builds a bridge between mesoscopic and microscopic magnetic structures.
Unitary neural networks are promising alternatives for solving the exploding and vanishing activation/gradient problem without the need for explicit normalization that reduces the inference speed. However, they often require longer training time due to the additional unitary constraints on their weight matrices. Here we show a novel algorithm using a backpropagation technique with Lie algebra for computing approximated unitary weights from their pre-trained, non-unitary counterparts. The unitary networks initialized with these approximations can reach the desired accuracies much faster, mitigating their training time penalties while maintaining inference speedups. Our approach will be instrumental in the adaptation of unitary networks, especially for those neural architectures where pre-trained weights are freely available.
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