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Perhaps the most exciting promise of the Rubin Observatory Legacy Survey of Space and Time (LSST) is its capability to discover phenomena never before seen or predicted from theory: true astrophysical novelties, but the ability of LSST to make these discoveries will depend on the survey strategy. Evaluating candidate strategies for true novelties is a challenge both practically and conceptually: unlike traditional astrophysical tracers like supernovae or exoplanets, for anomalous objects the template signal is by definition unknown. We present our approach to solve this problem, by assessing survey completeness in a phase space defined by object color, flux (and their evolution), and considering the volume explored by integrating metrics within this space with the observation depth, survey footprint, and stellar density. With these metrics, we explore recent simulations of the Rubin LSST observing strategy across the entire observed footprint and in specific regions in the Local Volume: the Galactic Plane and Magellanic Clouds. Under our metrics, observing strategies with greater diversity of exposures and time gaps tend to be more sensitive to genuinely new phenomena, particularly over time-gap ranges left relatively unexplored by previous surveys. To assist the community, we have made all the tools developed publicly available. Extension of the scheme to include proper motions and the detection of associations or populations of interest, will be communicated in paper II of this series. This paper was written with the support of the Vera C. Rubin LSST Transients and Variable Stars and Stars, Milky Way, Local Volume Science Collaborations., Comment: This paper was submitted to the ApJ Supplements Focus Issue on Rubin LSST Survey Strategy and supports considerations included in the Rubin Cadence Note https://docushare.lsst.org/docushare/dsweb/Get/Document-37653/Anomalies.pdf . Comments are welcome

For better user satisfaction and business effectiveness, more and more attention has been paid to the sequence-based recommendation system, which is used to infer the evolution of users' dynamic preferences, and recent studies have noticed that the evolution of users' preferences can be better understood from the implicit and explicit feedback sequences. However, most of the existing recommendation techniques do not consider the noise contained in implicit feedback, which will lead to the biased representation of user interest and a suboptimal recommendation performance. Meanwhile, the existing methods utilize item sequence for capturing the evolution of user interest. The performance of these methods is limited by the length of the sequence, and can not effectively model the long-term interest in a long period of time. Based on this observation, we propose a novel CTR model named denoising user-aware memory network (DUMN). Specifically, the framework: (i) proposes a feature purification module based on orthogonal mapping, which use the representation of explicit feedback to purify the representation of implicit feedback, and effectively denoise the implicit feedback; (ii) designs a user memory network to model the long-term interests in a fine-grained way by improving the memory network, which is ignored by the existing methods; and (iii) develops a preference-aware interactive representation component to fuse the long-term and short-term interests of users based on gating to understand the evolution of unbiased preferences of users. Extensive experiments on two real e-commerce user behavior datasets show that DUMN has a significant improvement over the state-of-the-art baselines. The code of DUMN model has been uploaded as an additional material.

Current and future optical and near-infrared wide-field surveys have the potential of finding kilonovae, the optical and infrared counterparts to neutron star mergers, independently of gravitational-wave or high-energy gamma-ray burst triggers. The ability to discover fast and faint transients such as kilonovae largely depends on the area observed, the depth of those observations, the number of re-visits per field in a given time frame, and the filters adopted by the survey; it also depends on the ability to perform rapid follow-up observations to confirm the nature of the transients. In this work, we assess kilonova detectability in existing simulations of the LSST strategy for the Vera C. Rubin Wide Fast Deep survey, with focus on comparing rolling to baseline cadences. Although currently available cadences can enable the detection of more than 300 kilonovae out to 1400 Mpc over the ten-year survey, we can expect only 3-32 kilonovae similar to GW170817 to be recognizable as fast-evolving transients. We also explore the detectability of kilonovae over the plausible parameter space, focusing on viewing angle and ejecta masses. We find that observations in redder izy bands are crucial for identification of nearby (within 300 Mpc) kilonovae that could be spectroscopically classified more easily than more distant sources. Rubin's potential for serendipitous kilonova discovery could be increased by gain of efficiency with the employment of individual 30s exposures (as opposed to 2x15s snap pairs), with the addition of red-band observations coupled with same-night observations in g- or r-bands, and possibly with further development of a new rolling-cadence strategy., Comment: Submitted to ApJS

We prove lower bound for the first closed or Neumann nonzero eigenvalue of the Laplacian on a compact quaternion-K\"ahler manifold in terms of dimension, diameter, and scalar curvature lower bound. It is derived as large time implication of the modulus of continuity estimates for solutions of the heat equation. We also establish lower bound for the first Dirichlet eigenvalue in terms of geometric data, via a Laplace comparison theorem for the distance to the boundary function., Comment: Comments are welcome. arXiv admin note: text overlap with arXiv:2010.12792

A diffeomorphism f is called super exponential divergent if for every r>1, the lower limit of #Per_n(f)/r^n diverges to infinity as n tends to infinity, where Per_n(f) is the set of all periodic points of f with period n. This property is stronger than the usual super exponential growth of the number of periodic points. We show that for a three dimensional manifold M, there exists an open subset O of Diff^1(M) such that diffeomorphisms with super exponential divergent property form a dense subset of O in the C^1-topology. A relevant result of non super exponential divergence for diffeomorphisms in a locally generic subset of Diff^r(M) (r=1,2,...\infty) is also shown., Comment: 19 pages, 1 figure