18,627 research outputs found
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 (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 with ,
, 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
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