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Hierarchical massive quadruple systems are ideal laboratories for examining the theories of star formation, dynamical evolution, and stellar evolution. The successive mergers of hierarchical quadruple systems might explain the mass gap between neutron stars and black holes. Looking for light curves of O-type binaries identified by LAMOST, we find a (2+2) quadruple system: TYC 3340-2437-1, located in the stellar bow-shock nebula (SBN). It has a probability of over 99.99\% being a quadruple system derived from the surface density of the vicinity stars. Its inner orbital periods are 3.390602(89) days and 2.4378(16) days, respectively, and the total mass is about (11.47 + 5.79) + (5.2 + 2.02) = 24.48 $M_{\odot}$. The line-of-sight inclinations of the inner binaries, B$_1$ and B$_2$, are 55.94 and 78.2 degrees, respectively, indicating that they are not co-planar. Based on observations spanning 34 months and the significance of the astrometric excess noise ($D>2$) in Gaia DR3 data, we guess that its outer orbital period might be a few years. If it were true, the quadruple system might form through the disk fragmentation mechanism with outer eccentric greater than zero. This eccentricity could be the cause of both the arc-like feature of the SBN and the noncoplanarity of the inner orbit. The outer orbital period and outer eccentric could be determined with the release of future epoch astrometric data of Gaia.

LAMOST-MRS-B is one of the sub-surveys of LAMOST medium-resolution (R~7500) spectroscopic survey. It aims at studying the statistical properties (e.g., binary fraction, orbital period distribution, mass ratio distribution) of binary stars and exotic stars. We intend to observe about 30000 stars (10 mag <= G <= 14.5 mag) with at least 10 visits in five years. We first planned to observe 25 plates around the galactic plane in 2018. Then the plates were reduced to 12 in 2019 because of the limitation of observation. At the same time, two new plates located at the high galactic latitude were added to explore binary properties influenced by the different environments. In this survey project, we set the identified exotic and low-metallicity stars with the highest observation priorities. For the rest of the selected stars, we gave higher priority to the relatively brighter stars in order to obtain high-quality spectra as many as possible. Spectra of 49129 stars have been obtained in LAMOST-MRS-B field and released in DR8, of which 28828 and 3375 stars have been visited more than twice and ten times with SNR >= 10, respectively. Most of the sources are B-, A-, and F-type stars with 0.6 < [Fe/H] < 0.4 dex. We also obtain 347 identified variable and exotic stars and about 250 stars with [Fe/H] < 1 dex. We measure radial velocities (RVs) by using 892233 spectra of the stars. The uncertainties of RV achieve about 1 km/s and 10 km/s1 for 95% of late- and early-type stars, respectively. The datasets presented in this paper are available at http://www.doi.org/10.57760/sciencedb.j00113.00035.

We evaluate the impact of probabilistically-constructed digital identity data collected from Sep. to Dec. 2017 (approx.), in the context of Lookalike-targeted campaigns. The backbone of this study is a large set of probabilistically-constructed "identities", represented as small bags of cookies and mobile ad identifiers with associated metadata, that are likely all owned by the same underlying user. The identity data allows to generate "identity-based", rather than "identifier-based", user models, giving a fuller picture of the interests of the users underlying the identifiers. We employ off-policy techniques to evaluate the potential of identity-powered lookalike models without incurring the risk of allowing untested models to direct large amounts of ad spend or the large cost of performing A/B tests. We add to historical work on off-policy evaluation by noting a significant type of "finite-sample bias" that occurs for studies combining modestly-sized datasets and evaluation metrics involving rare events (e.g., conversions). We illustrate this bias using a simulation study that later informs the handling of inverse propensity weights in our analyses on real data. We demonstrate significant lift in identity-powered lookalikes versus an identity-ignorant baseline: on average ~70% lift in conversion rate. This rises to factors of ~(4-32)x for identifiers having little data themselves, but that can be inferred to belong to users with substantial data to aggregate across identifiers. This implies that identity-powered user modeling is especially important in the context of identifiers having very short lifespans (i.e., frequently churned cookies). Our work motivates and informs the use of probabilistically-constructed identities in marketing. It also deepens the canon of examples in which off-policy learning has been employed to evaluate the complex systems of the internet economy., Comment: Accepted by WSDM 2019

The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. \cite{CGR}, replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems. In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant.

In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once an algorithm is proved to be bounded perturbation resilience, superiorizion can be used, and this allows flexibility in choosing the bounded perturbations in order to obtain a superior solution, as well explained in the paper. We also discuss some inertial extragradient methods. Under mild and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed extragradient and subgradient extragradient methods is proved. In addition we show that the perturbed algorithms converges at the rate of $O(1/t)$. Numerical illustrations are given to demonstrate the performances of the algorithms., Comment: Accepted for publication in The Journal of Inequalities and Applications. arXiv admin note: text overlap with arXiv:1711.01936 and text overlap with arXiv:1507.07302 by other authors

In this paper we study the bounded perturbation resilience of projection and contraction algorithms for solving variational inequality (VI) problems in real Hilbert spaces. Under typical and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed projection and contraction algorithms is proved. Based on the bounded perturbed resilience of projection and contraction algorithms, we present some inertial projection and contraction algorithms. In addition we show that the perturbed algorithms converges at the rate of $O(1/t)$., Comment: This paper is accepted for publication in Journal of Fixed Point Theory and Applications. arXiv admin note: text overlap with arXiv:1711.01937, and text overlap with arXiv:1507.07302 by other authors