A collaboration between the W. M. Keck Observatory (WMKO) in Hawaii and the NASA Exoplanet Science Institute (NExScI) in California, the Keck Observatory Archive (KOA) was commissioned in 2004 to archive observing data from WMKO, which operates two c
lassically scheduled 10 m ground-based telescopes. The observing data from Keck is not suitable for direct ingestion into the archive since the metadata contained in the original FITS headers lack the information necessary for proper archiving. Coupled with different standards among instrument builders and the heterogeneous nature of the data inherent in classical observing, in which observers have complete control of the instruments and their observations, the data pose a number of technical challenges for KOA. We describe the methodologies and tools that we have developed to successfully address these difficulties, adding content to the FITS headers and retrofitting the metadata in order to support archiving Keck data, especially those obtained before the archive was designed. With the expertise gained from having successfully archived observations taken with all eight currently active instruments at WMKO, we have developed lessons learned from handling this complex array of heterogeneous metadata that help ensure a smooth ingestion of data not only for current but also future instruments, as well as a better experience for the archive user.
Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG), in which the real spin, orbital pseudospin and layer pseudospins of the lowest Landau level form sponta
neous ordering. We observe intermediate quantum Hall plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only the in presence of an interlayer potential U. In the phase space of U and filling factor, we observe an intriguing hexagon pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.
This paper studies the problem of accurately recovering a sparse vector $beta^{star}$ from highly corrupted linear measurements $y = X beta^{star} + e^{star} + w$ where $e^{star}$ is a sparse error vector whose nonzero entries may be unbounded and $w
$ is a bounded noise. We propose a so-called extended Lasso optimization which takes into consideration sparse prior information of both $beta^{star}$ and $e^{star}$. Our first result shows that the extended Lasso can faithfully recover both the regression as well as the corruption vector. Our analysis relies on the notion of extended restricted eigenvalue for the design matrix $X$. Our second set of results applies to a general class of Gaussian design matrix $X$ with i.i.d rows $oper N(0, Sigma)$, for which we can establish a surprising result: the extended Lasso can recover exact signed supports of both $beta^{star}$ and $e^{star}$ from only $Omega(k log p log n)$ observations, even when the fraction of corruption is arbitrarily close to one. Our analysis also shows that this amount of observations required to achieve exact signed support is indeed optimal.
