Weighted Best Local Approximation

In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the Lpspaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.     

关于点可数序列邻域网

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Contact-pair neighborhood theorem for submanifolds in symplectic pairs

Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q⊂Mbe a codimension 2 compact submanifold. We show some sufficient and necessary conditions on the existence of the structure of contact pair (α,β) on Q,which is a pair of 1-forms of constant classes whose characteristic foliations are transverse and complementary such that α and β restrict to contact forms on the leaves of the characteristic foliations of βand α,respectively. This is a generalization of the neighborhood theorem for contact-type hypersurfaces in symplectic topology.     

On the expected surface area of the Wiener sausage

For parallel neighborhoods of the paths of the d ‐dimensional Brownian motion, so‐called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by means of geometric arguments that the expected surface area is equal to the first derivative of the mean volume of the Wiener sausage with respect to its radius (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

[a,b]-对等图的范-型条件

既是[a,b]-覆盖又是[a,b]-消去的图称为[a,b]-对等图.设1≤aan+1a+b,则G为[a,b]-对等图.给出了一个图是[a,b]-对等图的关于范-型条件及邻域并的若干充分条件,并指出定理中的条件在一定意义上是最好可能的.     

SKLOF:一种新的超新星候选范围约减算法

超新星是宇宙学中的“标准烛光”, 其在星系中爆发的概率很低, 是一种特殊、稀少的天体, 只有在大量观测的星系数据中才有机会遇到, 而正处于爆发期的超新星会照亮其整个星系从而在观测获得的星系光谱中具有较明显的特征。但是, 目前已发现的超新星数量相对于大量的天体而言又是非常稀少的, 搜寻它们所用的计算时间成为能否进行后续观测的关键, 因此需要寻找高效率的超新星搜寻方法。对超新星候选范围进行约减的LOF算法的时间复杂度较高, 计算量大, 不适用于大规模数据集。为此通过对LOF算法进行改进, 提出了一种在海量星系光谱中快速约减超新星候范围的新方法(SKLOF)。首先对光谱数据集中离中心点近的数据点进行数据剪枝, 剪掉那些肯定不是超新星候选体的光谱数据对象, 然后利用改进的LOF算法计算剩余的光谱数据的孤立性因子并降序排列进行离群搜索, 最后获得超新星候选体的较小的搜索范围以便进行后续的证认。实验结果表明, 该算法十分有效, 不仅在精确度上有所提高, 而且相比于LOF算法还进一步缩短了算法的运行时间, 提高了算法的执行效率。     

一种校正相位测量轮廓术量化误差的算法

为了减小相位测量轮廓术中因数字化设备内部结构的量化处理过程引起的相位量化误差,提高相位测量精度。针对相位测量精度要求较高且表面凹凸变化不大的被扫描物体提出了一种能够有效校正相位测量轮廓术量化误差的算法,测量相位中的每一个像素点利用其相邻像素点进行校正。实验结果显示,校正之后,相位量化误差标准差减小了41.38%,相位测量的精度得到了提高。     

Multi-Scale Aggregation Graph Neural Networks Based on Feature Similarity for Semi-Supervised Learning

The problem of extracting meaningful data through graph analysis spans a range of different fields, such as social networks, knowledge graphs, citation networks, the World Wide Web, and so on. As increasingly structured data become available, the importance of being able to effectively mine and learn from such data continues to grow. In this paper, we propose the multi-scale aggregation graph neural network based on feature similarity (MAGN), a novel graph neural network defined in the vertex domain. Our model provides a simple and general semi-supervised learning method for graph-structured data, in which only a very small part of the data is labeled as the training set. We first construct a similarity matrix by calculating the similarity of original features between all adjacent node pairs, and then generate a set of feature extractors utilizing the similarity matrix to perform multi-scale feature propagation on graphs. The output of multi-scale feature propagation is finally aggregated by using the mean-pooling operation. Our method aims to improve the model representation ability via multi-scale neighborhood aggregation based on feature similarity. Extensive experimental evaluation on various open benchmarks shows the competitive performance of our method compared to a variety of popular architectures.     

Modified DM Models for Aging Networks Based on Neighborhood Connectivity

Two modified Dorogovtsev-Mendes （DM） models of aging networks based on the dynamics of connecting nearest-neighbors are introduced. One edge of the new site is connected to the old site with probability - kt^-α as in the DM＇s model, where the degree and age of the old site are k and t, respectively. We consider two cases, i.e. the other edges of the new site attaching to the nearest-neighbors of the old site with uniform and degree connectivity probability, respectively. The network structure changes with an increase of aging exponent α It is found that the networks can produce scale-free degree distributions with small-world properties. And the different connectivity probabilities lead to the different properties of the networks.     

Efficient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT: Experimental Evaluation

For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most effective approaches. Most of the local search algorithms are based on the 1-flip neighborhood, which is the set of solutions obtainable by flipping the truth assignment of one variable. In this paper, we consider r-flip neighborhoods for r = 2, 3, and examine their effectiveness by computational experiments. In the accompanying paper, we proposed new implementations of these neighborhoods, and showed that the expected size of 2-flip neighborhood is O(n + m) and that of 3-flip neighborhood is O(m + t ² n), compared to their original size O(n ²) andO(n ³), respectively, where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. These are used in this paper under the framework of tabu search and other metaheuristic methods, and compared with other existing algorithms with 1-flip neighborhood. The results exhibit good prospects of larger neighborhoods.