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Stabilizing nitrogen-rich compound crystals under conventional conditions is a key issue in the development and application of high-energy density materials (HEDMs). Herein, a two-dimensional double-layer interlocked Li4(N5)2 nitrogen-rich compound crystals, in which the two N5 rings are locked to by sharing four Li atoms, was found to maintain structural stability at zero pressure conditions. Dynamics studies reliably confirm crystal stability below 250 K. Furthermore, the stability of Li4(N5)2 crystal mainly arises from the ionic interaction between Li atoms and N5 rings, formed by the charge transfer from Li atoms to N5 rings. This study highlights the feasibility of stabilizing nitrogen-rich compound crystals under conventional conditions, paving the way for atomic level advancements in HEDMs., Comment: 13 pages, 3 figures

Quantum metric, a probe to spacetime of the Hilbert space, has been found measurable in the nonlinear electronic transport and attracted tremendous interest. We show that the quantum metric is only a tip of the iceberg, by deriving unknown 11 out of 14 formulas of the quadratic nonlinear conductivity under the same symmetry that the quantum metric emerges. The formulas allow us to determine nonzero nonlinear conductivity elements for the magnetic point groups, calculate the quadratic nonlinear conductivity for arbitrary Hamiltonian, e.g., the even-layered MnBi$_2$Ti$_4$ thin films with and without the $C_{3}$ symmetry, and formulate scaling laws at the order of quantum metric to distinguish different mechanisms in the recent experiments. The theory is a comprehensive description of the quadratic nonlinear transport and will facilitate future experiments and applications., Comment: 6 pages, 3 figures, 3 tables

Online bidding and auction are crucial aspects of the online advertising industry. Conventionally, there is only one slot for ad display and most current studies focus on it. Nowadays, multi-slot display advertising is gradually becoming popular where many ads could be displayed in a list and shown as a whole to users. However, multi-slot display advertising leads to different cost-effectiveness. Advertisers have the incentive to adjust bid prices so as to win the most economical ad positions. In this study, we introduce bid shading into multi-slot display advertising for bid price adjustment with a Multi-task End-to-end Bid Shading(MEBS) method. We prove the optimality of our method theoretically and examine its performance experimentally. Through extensive offline and online experiments, we demonstrate the effectiveness and efficiency of our method, and we obtain a 7.01% lift in Gross Merchandise Volume, a 7.42% lift in Return on Investment, and a 3.26% lift in ad buy count.

A topological insulator is a quantum material which possesses conducting surfaces and an insulating bulk. Despite extensive researches on the properties of Dirac surface states, the characteristics of bulk states have remained largely unexplored. Here we report the observation of spinor-dominated magnetoresistance anomalies in the topological insulator $\beta $-Ag$_2$Se, induced by a magnetic-field-driven band topological phase transition. These anomalies are caused by intrinsic orthogonality in the wave-function spinors of the last Landau bands of the bulk states, in which backscattering is strictly forbidden during a band topological phase transition. This new type of longitudinal magnetoresistance, purely controlled by the wave-function spinors of the last Landau bands, highlights a unique signature of electrical transport around the band topological phase transition. With further reducing the quantum limit and gap size in $\beta $-Ag$_2$Se, our results may also suggest possible device applications based on this spinor-dominated mechanism and signify a rare case where topology enters the realm of magnetoresistance control., Comment: 16 pages, 4 figures; Version of original submission

How to stabilize nitrogen-rich high-energy-density molecules under conventional conditions is particularly important for the energy storage and conversion of such systems and has attracted extensive attention. In this work, our theoretical study showed for the first time that the stabilization mechanism of the nitrogen ring conformed to the superatomic properties at the atomic level. This result occurred because the stabilized anionic nitrogen rings generally showed planar high symmetry and the injected electrons occupied the superatomic molecular orbitals (SAMOs) of the nitrogen rings. According to these results, we identified the typical stabilized anionic nitrogen ring structures N64-, N5- and N42-, and their superatomic electronic configurations were 1S21P41D41F22S21P21F21D42P41G41F4, 1S21P41D41P22S21F41D42P4 and 1S21P41D21P21D22S22P41D4, respectively. On this basis, we further designed a pathway to stabilize nitrogen rings by introducing metal atoms as electron donors to form neutral ThN6, LiN5 and MgN4 structures, thereby replacing the anionization of systems. Our study highlights the importance of developing nitrogen-rich energetic materials from the perspective of superatoms., Comment: 6 pages, 3 figures