Energy Levels and Radiative Rates for Transitions in F-like Sc~XIII and Ne-like Sc~XII and Y~XXX

Energy levels, radiative rates and lifetimes are reported for F-like Sc~XIII and Ne-like Sc~XII and Y~XXX for which the general-purpose relativistic atomic structure package ({\sc grasp}) has been adopted. For all three ions limited data exist in the literature but comparisons have been made wherever possible to assess the accuracy of the calculations. In the present work the lowest 102, 125 and 139 levels have been considered for the respective ions. Additionally, calculations have also been performed with the flexible atomic code ({\sc fac}) to (particularly) confirm the accuracy of energy levels.Comment: 24pp of Text including 12 Tables will appear in Atoms 6 (2018

Discrepancies in Atomic Data and Suggestions for their Resolutions

The analysis and modelling of a range of plasmas (for example: astrophysical, laser-produced and fusion), require atomic data for a number of parameters, such as energy levels, radiative rates and electron impact excitation rates, or equivalently the effective collision strengths. Such data are desired for a wide range of elements and their many ions, although all elements are not useful for all types of plasmas. Since measurements of atomic data are mostly confined to only a few energy levels of some ions, calculations for all parameters are highly important. However, often there are large discrepancies among different calculations for almost all parameters, which makes it difficult to apply the data with confidence. Many such discrepancies (and the possible remedies) were discussed earlier (Fusion Sci. Tech. 2013, 63, 363). Since then a lot more anomalies for almost all of these atomic parameters have come to notice. Therefore, this paper is a revisit of various atomic parameters to highlight the large discrepancies, their possible sources and some suggestions to avoid those, so that comparatively more accurate and reliable atomic data may be available in the future.Comment: 18 pages of text including 7 figures will appear in Atoms 5 (2017

Revisiting the Sanders-Freiman-Ruzsa Theorem in Fpn\mathbb{F}_p^n and its Application to Non-malleable Codes

Non-malleable codes (NMCs) protect sensitive data against degrees of corruption that prohibit error detection, ensuring instead that a corrupted codeword decodes correctly or to something that bears little relation to the original message. The split-state model, in which codewords consist of two blocks, considers adversaries who tamper with either block arbitrarily but independently of the other. The simplest construction in this model, due to Aggarwal, Dodis, and Lovett (STOC'14), was shown to give NMCs sending k-bit messages to $O(k^7)$-bit codewords. It is conjectured, however, that the construction allows linear-length codewords. Towards resolving this conjecture, we show that the construction allows for code-length $O(k^5)$. This is achieved by analysing a special case of Sanders's Bogolyubov-Ruzsa theorem for general Abelian groups. Closely following the excellent exposition of this result for the group $\mathbb{F}_2^n$ by Lovett, we expose its dependence on $p$ for the group $\mathbb{F}_p^n$, where $p$ is a prime