24,409 research outputs found
Symmetries of geometric flows
By applying the theory of group-invariant solutions we investigate the
symmetries of Ricci flow and hyperbolic geometric flow both on Riemann
surfaces. The warped products on of both flows are also
studied.Comment: 27 page
Long time well-posdness of the Prandtl equations in Sobolev space
In this paper, we study the long time well-posedness for the nonlinear
Prandtl boundary layer equation on the half plane. While the initial data are
small perturbations of some monotonic shear profile, we prove the existence,
uniqueness and stability of solutions in weighted Sobolev space by energy
methods. The key point is that the life span of the solution could be any large
as long as its initial date is a perturbation around the monotonic shear
profile of small size like . The nonlinear cancellation properties of
Prandtl equations under the monotonic assumption are the main ingredients to
establish a new energy estimate.Comment: In this version, reviser some typos, 43 page
AutoEncoder Inspired Unsupervised Feature Selection
High-dimensional data in many areas such as computer vision and machine
learning tasks brings in computational and analytical difficulty. Feature
selection which selects a subset from observed features is a widely used
approach for improving performance and effectiveness of machine learning models
with high-dimensional data. In this paper, we propose a novel AutoEncoder
Feature Selector (AEFS) for unsupervised feature selection which combines
autoencoder regression and group lasso tasks. Compared to traditional feature
selection methods, AEFS can select the most important features by excavating
both linear and nonlinear information among features, which is more flexible
than the conventional self-representation method for unsupervised feature
selection with only linear assumptions. Experimental results on benchmark
dataset show that the proposed method is superior to the state-of-the-art
method.Comment: accepted by ICASSP 201
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