Godel Universe from String Theory

G\"odel universe is a direct product of a line and a three-dimensional spacetime we call G$_\alpha$. In this paper, we show that the G\"odel metrics can arise as exact solutions in Einstein-Maxwell-Axion, Einstein-Proca-Axion, or Freedman-Schwarz gauged supergravity theories. The last allows us to embed G\"odel universe in string theory. The ten-dimensional spacetime is a direct product of a line and the nine-dimensional one of an $S^3\times S^3$ bundle over G$_\alpha$, and it can be interpreted as some decoupling limit of the rotating D1/D5/D5 intersection. For some appropriate parameter choice, the nine-dimensional metric becomes an AdS$_3\times S^3$ bundle over squashed 3-sphere. We also study the properties of the G\"odel black holes that are constructed from the double Wick rotations of the G\"odel metrics.Comment: latex, 20 pages, discussion on null-energy condition included, typos corrected and references adde

Ethyl 4-methyl-1,3-dioxo-1,2,3,4-tetra­hydro­isoquinoline-4-carboxyl­ate

In the title compound, C13H13NO4, the fused-ring system is nearly planar, with an r.m.s. deviation of 0.0408 Å. In the crystal, mol­ecules are linked into centrosymmetric dimers by a pair of N—H⋯O hydrogen bonds. The ethyl group is disordered over two positions in a ratio of 0.758 (6):0.242 (6)

Existence of positive solution for a third-order three-point BVP with sign-changing Green's function

By using the Guo-Krasnoselskii fixed point theorem, we investigate the following third-order three-point boundary value problem $$\left\{ \begin{array}{l} u'''(t)=f(t,u(t)),\ t\in [0,1], \\ u'(0)=u(1)=0,\ u''(\eta)+\alpha u(0)=0, \end{array} \right.$$ where $\alpha \in [0,2)$ and $\eta\in[\frac{\sqrt{121+24\alpha}-5}{3(4+\alpha)},1)$. The emphasis is mainly that although the corresponding Green's function is sign-changing, the solution obtained is still positive

Resilient neural network training for accelerators with computing errors

—With the advancements of neural networks, customized accelerators are increasingly adopted in massive AI applications. To gain higher energy efficiency or performance, many hardware design optimizations such as near-threshold logic or overclocking can be utilized. In these cases, computing errors may happen and the computing errors are difficult to be captured by conventional training on general purposed processors (GPPs). Applying the offline trained neural network models to the accelerators with errors directly may lead to considerable prediction accuracy loss. To address this problem, we explore the resilience of neural network models and relax the accelerator design constraints to enable aggressive design options. First of all, we propose to train the neural network models using the accelerators’ forward computing results such that the models can learn both the data and the computing errors. In addition, we observe that some of the neural network layers are more sensitive to the computing errors. With this observation, we schedule the most sensitive layer to the attached GPP to reduce the negative influence of the computing errors. According to the experiments, the neural network models obtained from the proposed training outperform the original models significantly when the CNN accelerators are affected by computing errors

{μ-6,6′-Dimeth­oxy-2,2′-[propane-1,3-diylbis(nitrilo­methyl­idyne)]diphenolato}trinitratocopper(II)erbium(III) acetone solvate

In the title complex, [CuEr(C19H20N2O4)(NO3)3]·CH3COCH3, the CuII ion is coordinated in a square-planar environment by two O atoms and two N atoms of a Schiff base ligand. The ErIII ion is bis-chelated by three nitrate ligands and coordinated by four O atoms of the Schiff base ligand in a slightly distorted bicapped square-anti­prismatic environment

Cooperative three- and four- player quantum games

A cooperative multi-player quantum game played by 3 and 4 players has been studied. Quantum superposed operator is introduced in this work which solves the non-zero sum difficulty in previous treatment. The role of quantum entanglement of the initial state is discussed in details.Comment: 7 pages with 3 figures. To appear in Physics Letters