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This is the first in a series of two papers where we analyze the transverse expansion of the metric on a general null hypersurface. In this paper we obtain general geometric identities relating the transverse derivatives of the ambient Ricci tensor and the transverse expansion of the metric at the null hypersurface. We also explore the case where the hypersurface exhibits a generalized symmetry generator, namely a privileged vector field in the ambient space which, at the hypersurface, is null and tangent (including the possibility of zeroes). This covers the Killing, homothetic, or conformal horizon cases, and, more generally, any situation where detailed information on the deformation tensor of the symmetry generator is available. Our approach is entirely covariant, independent on any field equations, and does not make any assumptions regarding the topology or dimension of the null hypersurface. As an application we prove that the full transverse expansion of the spacetime metric at a non-degenerate Killing horizon (also allowing for bifurcation surfaces) is uniquely determined in terms of abstract data on the horizon and the tower of derivatives of the ambient Ricci tensor at the horizon. In particular, the transverse expansion of the metric in $\Lambda$-vacuum spacetimes admitting a non-degenerate horizon is uniquely determined in terms of abstract data at the horizon., Comment: 42 pages

We report on the chemo-dynamical analysis of SPLUS J142445.34-254247.1, an extremely metal-poor halo star enhanced in elements formed by the rapid neutron-capture process. This star was first selected as a metal-poor candidate from its narrow-band S-PLUS photometry and followed up spectroscopically in medium-resolution with Gemini South/GMOS, which confirmed its low-metallicity status. High-resolution spectroscopy was gathered with GHOST at Gemini South, allowing for the determination of chemical abundances for 36 elements, from carbon to thorium. At [Fe/H]=-3.39, SPLUS J1424-2542 is one of the lowest metallicity stars with measured Th and has the highest logeps(Th/Eu) observed to date, making it part of the "actinide-boost" category of r-process enhanced stars. The analysis presented here suggests that the gas cloud from which SPLUS J1424-2542 was formed must have been enriched by at least two progenitor populations. The light-element (Z<=30) abundance pattern is consistent with the yields from a supernova explosion of metal-free stars with 11.3-13.4 Msun, and the heavy-element (Z>=38) abundance pattern can be reproduced by the yields from a neutron star merger (1.66Msun and 1.27Msun) event. A kinematical analysis also reveals that SPLUS J1424-2542 is a low-mass, old halo star with a likely in-situ origin, not associated with any known early merger events in the Milky Way., Comment: 26 pages, 11 figures, accepted for publication on ApJ

Pristine_183.6849+04.8619 (P1836849) is an extremely metal-poor ([Fe/H]$=-3.3\pm0.1$) star on a prograde orbit confined to the Galactic disk. Such stars are rare and may have their origins in protogalactic fragments that formed the early Milky Way, in low mass satellites accreted later, or forming in situ in the Galactic plane. Here we present a chemo-dynamical analysis of the spectral features between $3700-11000$\r{A} from a high-resolution spectrum taken during Science Verification of the new Gemini High-resolution Optical SpecTrograph (GHOST). Spectral features for many chemical elements are analysed (Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Fe, Ni), and valuable upper limits are determined for others (C, Na, Sr, Ba). This main sequence star exhibits several rare chemical signatures, including (i) extremely low metallicity for a star in the Galactic disk, (ii) very low abundances of the light $\alpha$-elements (Na, Mg, Si) compared to other metal-poor stars, and (iii) unusually large abundances of Cr and Mn, where [Cr, Mn/Fe]$_{\rm NLTE}>+0.5$. A comparison to theoretical yields from supernova models suggests that two low mass Population III objects (one 10 M$_\odot$ supernova and one 17 M$_\odot$ hypernova) can reproduce the abundance pattern well (reduced $\chi^2<1$). When this star is compared to other extremely metal-poor stars on quasi-circular, prograde planar orbits, differences in both chemistry and kinematics imply there is little evidence for a common origin. The unique chemistry of P1836849 is discussed in terms of the earliest stages in the formation of the Milky Way., Comment: 16 pages, 10 figures, 6 tables. Accepted by MNRAS November 22; Revisions include comparisons to more EMP stars, results unchanged

The Gemini High-resolution Optical SpecTrograph (GHOST) is the newest high resolution spectrograph to be developed for a large aperture telescope, recently deployed and commissioned at the Gemini-South telescope. In this paper, we present the first science results from the GHOST spectrograph taking during its commissioning runs. We have observed the bright metal-poor benchmark star HD 122563, along with two stars in the ultra faint dwarf galaxy, Ret II, one of which was previously identified as a candidate member, but did not have a previous detailed chemical abundance analysis. This star (GDR3 0928) is found to be a bona fide member of Ret II, and from a spectral synthesis analysis, it is also revealed to be a CEMP-r star, with significant enhancements in the several light elements (C, N, O, Na, Mg, and Si), in addition to featuring an r-process enhancement like many other Ret II stars. The light-element enhancements in this star resemble the abundance patterns seen in the CEMP-no stars of other ultra faint dwarf galaxies, and are thought to have been produced by an independent source from the r-process. These unusual abundance patterns are thought to be produced by faint supernovae, which may be produced by some of the earliest generations of stars., Comment: 23 pages, 9 figures, 7 tables, submitted to the AAS Journals

The characteristic Cauchy problem of the Einstein field equations has been recently addressed from a completely abstract viewpoint by means of hypersurface data and, in particular, via the notion of double null data. However, this definition was given in a partially gauge-fixed form. In this paper we generalize the notion of double null data in a fully diffeomorphism and gauge covariant way, and show that the definition is complete by proving that no extra conditions are needed to embed the double null data in some spacetime. The second aim of the paper is to show that the characteristic Cauchy problem satisfies a geometric uniqueness property. Specifically, we introduce a natural notion of isometry at the abstract level such that two double null data that are isometric in this sense give rise to isometric spacetimes., Comment: 36 pages, 1 figure

Short-range ordering in cation-disordered cathodes can have a significant effect on their electrochemical properties. Here, we characterise the cation short-range order in the antiperovskite cathode material Li$_2$FeSO, using density functional theory, Monte Carlo simulations, and synchrotron X-ray pair-distribution-function data. We predict partial short-range cation-ordering, characterised by favourable OLi$_4$Fe$_2$ oxygen coordination with a preference for polar cis-OLi$_4$Fe$_2$ over non-polar trans-OLi$_4$Fe$_2$ configurations. This preference for polar cation configurations produces long-range disorder, in agreement with experimental data. The predicted short-range-order preference contrasts with that for a simple point-charge model, which instead predicts preferential trans-OLi$_4$Fe$_2$ oxygen coordination and corresponding long-range crystallographic order. The absence of long-range order in Li$_2$FeSO can therefore be attributed to the relative stability of cis-OLi$_4$Fe$_2$ and other non-OLi$_4$Fe$_2$ oxygen-coordination motifs. We show that this effect is associated with the polarisation of oxide and sulfide anions in polar coordination environments, which stabilises these polar short-range cation orderings. We propose similar anion-polarisation-directed short-range-ordering may be present in other heterocationic materials that contain cations with different formal charges. Our analysis also illustrates the limitations of using simple point-charge models to predict the structure of cation-disordered materials, where other factors, such as anion polarisation, may play a critical role in directing both short- and long-range structural correlations.

General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this formalism, we formulate and solve in a completely abstract way the characteristic Cauchy problem of the Einstein vacuum field equations. The initial data is detached from any spacetime notion, and it is fully diffeomorphism and gauge covariant. The results of this paper put the characteristic problem on a similar footing as the standard Cauchy problem in General Relativity., Comment: The presentation of the proof of Theorem 7.15 has been improved. Several typos has been amended. Some long computations has been moved to appendices

In this work, we compute the time-dependent masses that govern the dynamics of scalar and tensor perturbations propagating on an effective flat, homogeneous, and isotropic background within the framework of loop quantum cosmology, regularized according to the procedure put forward by Dapor and Liegener. To do so, we follow the two main approaches that, in the field of loop quantum cosmology, lead to hyperbolic equations for the perturbations in the ultraviolet sector: the hybrid and dressed metric formalisms. This allows us to compare the masses resulting from both proposals and analyze their positivity in regimes of physical interest: the big bounce and the contracting de Sitter phase in the asymptotic past that is a defining feature of the model under consideration., Comment: 25 pages, 5 figures

In this paper, we introduce a new benchmark dataset named IPN Hand with sufficient size, variety, and real-world elements able to train and evaluate deep neural networks. This dataset contains more than 4,000 gesture samples and 800,000 RGB frames from 50 distinct subjects. We design 13 different static and dynamic gestures focused on interaction with touchless screens. We especially consider the scenario when continuous gestures are performed without transition states, and when subjects perform natural movements with their hands as non-gesture actions. Gestures were collected from about 30 diverse scenes, with real-world variation in background and illumination. With our dataset, the performance of three 3D-CNN models is evaluated on the tasks of isolated and continuous real-time HGR. Furthermore, we analyze the possibility of increasing the recognition accuracy by adding multiple modalities derived from RGB frames, i.e., optical flow and semantic segmentation, while keeping the real-time performance of the 3D-CNN model. Our empirical study also provides a comparison with the publicly available nvGesture (NVIDIA) dataset. The experimental results show that the state-of-the-art ResNext-101 model decreases about 30% accuracy when using our real-world dataset, demonstrating that the IPN Hand dataset can be used as a benchmark, and may help the community to step forward in the continuous HGR. Our dataset and pre-trained models used in the evaluation are publicly available at https://github.com/GibranBenitez/IPN-hand., Comment: Accepted at ICPR 2020

In order to cope with the ever increasing traffic load that networks will need to support, a new approach for planning cellular networks deployments should be followed. Traditionally, cell association and resource allocation has been based on the received signal power but this approach seems to be inadequate regarding the brewing of heterogeneous networks. In this work, we first implement a network simulator in order to test new cell associacion and resource allocation techniques. Then, we pose the network utility maximisation problem, reformulating the Downlink and Uplink Decoupling (DUDe) scheme under the framework and tools of mathematical optimisation. We derive the explicit solution of the problem under fixed and non-fixed association policy so as to propose and develope both centralised and decentralised algorithms capable of solving cell association and resource allocation problems. We observe that the decentralised approach requires low computational effort and represents a significant gain in the overall performance of the network., Comment: 80 pages, Preliminary Version

Context. The most primitive metal-poor stars are important for studying the conditions of the early galaxy and are also relevant to big bang nucleosynthesis. Aims. Our objective is to find the brightest (V<14) most metal-poor stars. Methods. Candidates were selected using a new method, which is based on the mismatch between spectral types derived from colors and observed spectral types. They were observed first at low resolution with EFOSC2 at the NTT/ESO to obtain an initial set of stellar parameters. The most promising candidate, 2MASS J18082002-5104378 (V=11.9), was observed at high resolution (R=50 000) with UVES at the VLT/ESO, and a standard abundance analysis was performed. Results. We found that 2MASS J18082002-5104378 is an ultra metal-poor star with stellar parameters Teff = 5440 K, log g = 3.0 dex, vt = 1.5 km/s, [Fe/H] = -4.1 dex. The star has [C/Fe]<+0.9 in a 1D analysis, or [C/Fe]<=+0.5 if 3D effects are considered; its abundance pattern is typical of normal (non-CEMP) ultra metal-poor stars. Interestingly, the star has a binary companion. Conclusions. 2MASS J1808-5104 is the brightest (V=11.9) metal-poor star of its category, and it could be studied further with even higher S/N spectroscopy to determine additional chemical abundances, thus providing important constraints to the early chemical evolution of our Galaxy., Comment: A&A Letters