Lattice calculation of hadronic tensor of the nucleon

We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.Comment: 8 pages, 5 figures; Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Variance Reduction and Cluster Decomposition

It is a common problem in lattice QCD calculation of the mass of the hadron with an annihilation channel that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation of the three-point function and the calculation of the neutron electric dipole moment with the $\theta$ term suffer from a noise problem due to the $\sqrt{V}$ fluctuation. We identify these problems to have the same origin and the $\sqrt{V}$ problem can be overcome by utilizing the cluster decomposition principle. We demonstrate this by considering the calculations of the glueball mass, the strangeness content in the nucleon, and the CP violation angle in the nucleon due to the $\theta$ term. It is found that for lattices with physical sizes of 4.5 - 5.5 fm, the statistical errors of these quantities can be reduced by a factor of 3 to 4. The systematic errors can be estimated from the Akaike information criterion. For the strangeness content, we find that the systematic error is of the same size as that of the statistical one when the cluster decomposition principle is utilized. This results in a 2 to 3 times reduction in the overall error.Comment: 7 pages, 5 figures, appendix added to address the systematic erro

Neural Collaborative Ranking

Recommender systems are aimed at generating a personalized ranked list of items that an end user might be interested in. With the unprecedented success of deep learning in computer vision and speech recognition, recently it has been a hot topic to bridge the gap between recommender systems and deep neural network. And deep learning methods have been shown to achieve state-of-the-art on many recommendation tasks. For example, a recent model, NeuMF, first projects users and items into some shared low-dimensional latent feature space, and then employs neural nets to model the interaction between the user and item latent features to obtain state-of-the-art performance on the recommendation tasks. NeuMF assumes that the non-interacted items are inherent negative and uses negative sampling to relax this assumption. In this paper, we examine an alternative approach which does not assume that the non-interacted items are necessarily negative, just that they are less preferred than interacted items. Specifically, we develop a new classification strategy based on the widely used pairwise ranking assumption. We combine our classification strategy with the recently proposed neural collaborative filtering framework, and propose a general collaborative ranking framework called Neural Network based Collaborative Ranking (NCR). We resort to a neural network architecture to model a user's pairwise preference between items, with the belief that neural network will effectively capture the latent structure of latent factors. The experimental results on two real-world datasets show the superior performance of our models in comparison with several state-of-the-art approaches.Comment: Proceedings of the 2018 ACM on Conference on Information and Knowledge Managemen

Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs

The Hofstadter model, well-known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment [Science, 365, 1021 (2019)], we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to $\mathbb{Z}_2$ topological insulators. We conclude by discussing possible schemes for the experimental realizations of the models in photonic platforms