A higher-order approximation to a hybrid parabolic equation approach for density discontinuities

2017 ◽  
Vol 142 (4) ◽  
pp. 2526-2527
Author(s):  
Kevin B. Smith
Keyword(s):  
Parabolic Equation ◽  
Order Approximation ◽  
Higher Order ◽  
Equation Approach

scholarly journals Learning Graph Convolutional Network for Skeleton-Based Human Action Recognition by Neural Searching

2020 ◽  
Vol 34 (03) ◽  
pp. 2669-2676 ◽  
Author(s):  
Wei Peng ◽  
Xiaopeng Hong ◽  
Haoyu Chen ◽  
Guoying Zhao
Keyword(s):  
Action Recognition ◽  
Large Scale ◽  
Order Approximation ◽  
Human Action Recognition ◽  
Search Space ◽  
Human Action ◽  
Higher Order ◽  
Dynamic Graph ◽  
Convolutional Network ◽  
Representational Capacity

Human action recognition from skeleton data, fuelled by the Graph Convolutional Network (GCN) with its powerful capability of modeling non-Euclidean data, has attracted lots of attention. However, many existing GCNs provide a pre-defined graph structure and share it through the entire network, which can loss implicit joint correlations especially for the higher-level features. Besides, the mainstream spectral GCN is approximated by one-order hop such that higher-order connections are not well involved. All of these require huge efforts to design a better GCN architecture. To address these problems, we turn to Neural Architecture Search (NAS) and propose the first automatically designed GCN for this task. Specifically, we explore the spatial-temporal correlations between nodes and build a search space with multiple dynamic graph modules. Besides, we introduce multiple-hop modules and expect to break the limitation of representational capacity caused by one-order approximation. Moreover, a corresponding sampling- and memory-efficient evolution strategy is proposed to search in this space. The resulted architecture proves the effectiveness of the higher-order approximation and the layer-wise dynamic graph modules. To evaluate the performance of the searched model, we conduct extensive experiments on two very large scale skeleton-based action recognition datasets. The results show that our model gets the state-of-the-art results in term of given metrics.

Modeling of Long-Range Reverberation Signal for Rough Bottom Consisting of Polygon Facets

2018 ◽  
Vol 26 (04) ◽  
pp. 1850041
Author(s):  
Youngmin Choo ◽  
Woojae Seong
Keyword(s):  
Long Range ◽  
Order Approximation ◽  
Higher Order ◽  
Ocean Bottom ◽  
Analytic Surface ◽  
Surface Integral ◽  
Computational Burden ◽  
Analytic Integration ◽  
The Cost ◽  
Delay Difference

To acquire a stable reverberation signal from an irregular ocean bottom, we derive the analytic surface integral of a scattered signal using Stokes’ theorem while approximating the bottom using a combination of polygon facets. In this approach, the delay difference in the elemental scattering area is considered, while the representative delay is used for the elemental scattering area in the standard reverberation model. Two different reverberation models are applied to a randomly generated rough bottom, which is composed of triangular facets. Their results are compared, and the scheme using analytic integration shows a converged reverberation signal, even with a large elemental scattering area, at the cost of an additional computational burden caused by a higher order approximation in the surface integral of the scattered signals.

scholarly journals On Moore-Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Numerical Modeling ◽  
Computational Methods ◽  
Order Approximation ◽  
Higher Order ◽  
Benchmark Test ◽  
Essential Component ◽  
Stiffness Matrices ◽  
Penrose Pseudoinverse

Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.

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