474 research outputs found
A Hybridized Weak Galerkin Finite Element Scheme for the Stokes Equations
In this paper a hybridized weak Galerkin (HWG) finite element method for
solving the Stokes equations in the primary velocity-pressure formulation is
introduced. The WG method uses weak functions and their weak derivatives which
are defined as distributions. Weak functions and weak derivatives can be
approximated by piecewise polynomials with various degrees. Different
combination of polynomial spaces leads to different WG finite element methods,
which makes WG methods highly flexible and efficient in practical computation.
A Lagrange multiplier is introduced to provide a numerical approximation for
certain derivatives of the exact solution. With this new feature, HWG method
can be used to deal with jumps of the functions and their flux easily. Optimal
order error estimate are established for the corresponding HWG finite element
approximations for both {\color{black}primal variables} and the Lagrange
multiplier. A Schur complement formulation of the HWG method is derived for
implementation purpose. The validity of the theoretical results is demonstrated
in numerical tests.Comment: 19 pages, 4 tables,it has been accepted for publication in SCIENCE
CHINA Mathematics. arXiv admin note: substantial text overlap with
arXiv:1402.1157, arXiv:1302.2707 by other author
Towards Effective Codebookless Model for Image Classification
The bag-of-features (BoF) model for image classification has been thoroughly
studied over the last decade. Different from the widely used BoF methods which
modeled images with a pre-trained codebook, the alternative codebook free image
modeling method, which we call Codebookless Model (CLM), attracted little
attention. In this paper, we present an effective CLM that represents an image
with a single Gaussian for classification. By embedding Gaussian manifold into
a vector space, we show that the simple incorporation of our CLM into a linear
classifier achieves very competitive accuracy compared with state-of-the-art
BoF methods (e.g., Fisher Vector). Since our CLM lies in a high dimensional
Riemannian manifold, we further propose a joint learning method of low-rank
transformation with support vector machine (SVM) classifier on the Gaussian
manifold, in order to reduce computational and storage cost. To study and
alleviate the side effect of background clutter on our CLM, we also present a
simple yet effective partial background removal method based on saliency
detection. Experiments are extensively conducted on eight widely used databases
to demonstrate the effectiveness and efficiency of our CLM method
Towards Faster Training of Global Covariance Pooling Networks by Iterative Matrix Square Root Normalization
Global covariance pooling in convolutional neural networks has achieved
impressive improvement over the classical first-order pooling. Recent works
have shown matrix square root normalization plays a central role in achieving
state-of-the-art performance. However, existing methods depend heavily on
eigendecomposition (EIG) or singular value decomposition (SVD), suffering from
inefficient training due to limited support of EIG and SVD on GPU. Towards
addressing this problem, we propose an iterative matrix square root
normalization method for fast end-to-end training of global covariance pooling
networks. At the core of our method is a meta-layer designed with loop-embedded
directed graph structure. The meta-layer consists of three consecutive
nonlinear structured layers, which perform pre-normalization, coupled matrix
iteration and post-compensation, respectively. Our method is much faster than
EIG or SVD based ones, since it involves only matrix multiplications, suitable
for parallel implementation on GPU. Moreover, the proposed network with ResNet
architecture can converge in much less epochs, further accelerating network
training. On large-scale ImageNet, we achieve competitive performance superior
to existing counterparts. By finetuning our models pre-trained on ImageNet, we
establish state-of-the-art results on three challenging fine-grained
benchmarks. The source code and network models will be available at
http://www.peihuali.org/iSQRT-COVComment: Accepted to CVPR 201
Research on Urban End-Delivery Paths Considering the Consumer\u27s Delivery Time Demand
Delivery time is an increasingly important consideration in consumer behavior, and there are still some problems in the urban logistics and delivery industry in considering matching consumer demand and improving logistics and delivery efficiency to control enterprise costs. In this paper, we will construct an end delivery path model based on consumers\u27 delivery time preference, use ALNS algorithm to analyse the distribution routes of five real communities, and conclude that the total distribution cost increases and then decreases with the increase of the number of consumers who choose value-added services. In this paper, we use scientific methods to calculate and design distribution routes to reduce distribution costs and further satisfy consumer preferences. At the same time, from the perspective of the industry management department, delivery enterprises and the consumers, three main bodies, the next development direction is proposed for different main bodies to promote the high-quality development of urban logistics and delivery market
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