The build up of the correlation between halo spin and the large scale structure

Both simulations and observations have confirmed that the spin of haloes/galaxies is correlated with the large scale structure (LSS) with a mass dependence such that the spin of low-mass haloes/galaxies tend to be parallel with the LSS, while that of massive haloes/galaxies tend to be perpendicular with the LSS. It is still unclear how this mass dependence is built up over time. We use N-body simulations to trace the evolution of the halo spin-LSS correlation and find that at early times the spin of all halo progenitors is parallel with the LSS. As time goes on, mass collapsing around massive halo is more isotropic, especially the recent mass accretion along the slowest collapsing direction is significant and it brings the halo spin to be perpendicular with the LSS. Adopting the $fractional$ $anisotropy$ (FA) parameter to describe the degree of anisotropy of the large-scale environment, we find that the spin-LSS correlation is a strong function of the environment such that a higher FA (more anisotropic environment) leads to an aligned signal, and a lower anisotropy leads to a misaligned signal. In general, our results show that the spin-LSS correlation is a combined consequence of mass flow and halo growth within the cosmic web. Our predicted environmental dependence between spin and large-scale structure can be further tested using galaxy surveys.Comment: 9 pages, 7 figures, 2 tables, Accepted for publication in MNRA

Top-N Recommender System via Matrix Completion

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relaxation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strategy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level.Comment: AAAI 201

Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.Comment: Published in AAAI 201

Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary

We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are H\"older continuous up to the boundary provided that the scaled mixed norm $L^{p,q}_{x,t}$ with $3/p+2/q\leq 2, 2<q\le \infty$, $(p,q) \not = (3/2,\infty)$, is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some conditions of the Prodi-Serrin type