检索结果-内蒙古大学图书馆

arXiv 2017年

作者： Puccetti, Giovanni Rigo, Pietro Wang, Bin Wang, Ruodu Department of Economics Management and Quantitative Methods University of Milano Italy Department of Mathematics University of Pavia Italy Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Statistics and Actuarial Science University of Waterloo Waterloo Canada

In the recent years, the notion of mixability has been developed with applications to optimal transportation, quantitative finance and operations research. An n-tuple of distributions is said to be jointly mixable if there exist n random variables following these distributions and adding up to a constant, called center, with probability one. When the n distributions are identical, we speak of complete mixability. If each distribution has finite mean, the center is obviously the sum of the means. In this paper, we investigate the set of centers of completely and jointly mixable distributions not having a finite mean. In addition to several results, we show the (possibly counterintuitive) fact that, for each n ≥ 2, there exist n standard Cauchy random variables adding up to a constant C if and only if. Copyright © 2017, The Authors. All rights reserved.

关键词： random variables

来源：评论

学校读者我要写书评

暂无评论

Quantitative stability estimates for Fokker-Planck equations

arXiv

引用

arXiv 2017年

作者： Li, Huaiqian Luo, Dejun School of Mathematics Sichuan University Chengdu610064 China Key Laboratory of Random Complex Structures and Data Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of the Chinese Academy of Sciences Beijing100049 China

We consider the Fokker-Planck equations with irregular coefficients. Two different cases are treated: in the degenerate case, the coefficients are assumed to be weakly differentiable, while in the non-degenerate case the drift satisfies only the Ladyzhenskaya-Prodi-Serrin condition. Using Trevisan's superposition principle which represents the solution as the marginal of the solution to the martingale problem of the diffusion operator, we establish quantitative stability estimates for the solutions of Fokker-Planck *** Codes 35Q84, 60H10 Copyright © 2017, The Authors. All rights reserved.

关键词： Mechanics

来源：评论

学校读者我要写书评

暂无评论

Potts model based on a Markov process computation solves the community structure problem effectively

引用

Physical Review E 2012年第1期86卷 016109-016109页

作者： Hui-Jia Li Yong Wang Ling-Yun Wu Junhua Zhang Xiang-Sun Zhang Academy of Mathematics and Systems Science Chinese Academy of Science Beijing 100190 China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing 100190 China Key Laboratory of Random Complex Structures and Data Science Chinese Academy of Sciences Beijing 100190 China

The Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of the Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then we show that the local uniform behavior of spin values across multiple timescales in the representation of the Markov variables could naturally reveal the network's hierarchical community structure. In addition, critical topological information regarding multivariate spin configuration could also be inferred from the spectral signatures of the Markov process. Finally an algorithm is developed to determine fuzzy communities based on the optimal number of communities and the stability across multiple timescales. The effectiveness and efficiency of our algorithm are theoretically analyzed as well as experimentally validated.

关键词： Potts model

来源：评论

学校读者我要写书评

暂无评论

Pathwise uniqueness of multi-dimensional stochastic differential equations with H(o)lder diffusion coefficients

引用

中国数学前沿 2011年第1期6卷 129-136页

作者： Dejun LUO Key Lab of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We extend Yamada-Watababe's criterion [J. Math. Kyoto Univ.,1971, 11: 553-563] on the pathwise uniqueness of one-dimensional stochastic differential equations to a special class of multi-dimensional stochastic dif... 详细信息

关键词： Stochastic differential equation (SDE) strong solution pathwise uniqueness H(o)lder continuity

来源：评论

学校读者我要写书评

暂无评论

A dynamical method to extract communities induced by low or middle-degree nodes

A dynamical method to extract communities induced by low or ...

引用

5th IEEE International Conference on Systems Biology, ISB 2011

作者： Zhang, Junhua Liu, Zhi-Ping Zhang, Xiang-Sun Chen, Luonan Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Key Laboratory of Systems Biology Shanghai Institutes for Biological Sciences Chinese Academy of Sciences Shanghai 200032 China Key Laboratory of Management Decision and Information Systems Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing 100190 China

ISBN: (纸本)9781457716669

Many networks are proved to have community structure. Dense communities have been intensively investigated in recent years, oppositely seldom attention has been paid to sparse ones, which refer to those communities induced by low or middle-degree nodes rather than high-degree components. Recently, it has gradually been recognized that sparse community is also an important structure in biological networks because most disease genes and drug targets are within it. In this paper, we propose a dynamical method to extract sparse communities in complex networks by constructing local synchronization properties of phase oscillators. Compared to dense communities, sparse ones provide more general building and functional blocks in the networks without emphasis on the dominance of internal degrees over outside ones as well as the constraints of high degree connectors. © 2011 IEEE.

关键词： complex networks

来源：评论

学校读者我要写书评

暂无评论

A dynamical method to extract communities induced by low or middle-degree nodes

A dynamical method to extract communities induced by low or ...

引用

IEEE International Conference on Systems Biology

作者： Junhua Zhang Zhi-Ping Liu Xiang-Sun Zhang Luonan Chen Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences (CAS) Beijing China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences (CAS) Beijing China Chinese Academy of Sciences Beijing Beijing CN

ISBN: (纸本)9781457716614

关键词： Communities Diseases Drugs Synchronization complex networks Humans Proteins

来源：评论

学校读者我要写书评

暂无评论

DETECTING COMMUNITY STRUCTURE： FROM PARSIMONY TO WEIGHTED PARSIMONY

引用

Journal of Systems science & complexity 2010年第5期23卷 1024-1036页

作者： Junhua ZHANG Yuqing QIU Xiang-Sun ZHANG Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Community detection has attracted a great deal of attention in recent years. A parsimony criterion for detecting this structure means that as minimal as possible number of inserted and deleted edges is needed when we make the network considered become a disjoint union of cliques. However, many small groups of nodes are obtained by directly using this criterion to some networks especially for sparse ones. In this paper we propose a weighted parsimony model in which a weight coefficient is introduced to balance the inserted and deleted edges to ensure the obtained subgraphs to be reasonable communities. Some benchmark testing examples are used to validate the effectiveness of the proposed method. It is interesting that the weight here can be determined only by the topological features of the network. Meanwhile we make some comparison of our model with maximizing modularity Q and modularity density D on some of the benchmark networks, although sometimes too many or a little less numbers of communities are obtained with Q or D, a proper number of communities are detected with the weighted model. All the computational results confirm its capability for community detection for the small or middle size networks.

关键词： Cliques community detection complex networks parsimony.

来源：评论

学校读者我要写书评

暂无评论

On Resolution Limit of the Modularity in Community Detection

On Resolution Limit of the Modularity in Community Detection

引用

第九届运筹学及其应用国际研讨会

作者： Junhua Zhang Xiang-Sun Zhang Academy of Mathematics and Systems Science CAS Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science CAS

Modularity Q has been broadly used as a valid measure for community detection in complex networks. Fortunato and Barthe ′lemy later proposed that modularity contains an intrinsic scale that depends on the total number of links in the network. But some extra restrictions on some parameters are needed for their analysis. In this paper we further study this problem. Here we give general analysis and more details to show that the resolution limit of Q depends not only on the total links but also on the degree of interconnectedness between pairs of communities. Without any constraint imposed on the parameters, there exists a proper area of the validity (or invalidity) of Q, which is deduced by the definitions of community structure and modularity Q, all these make the analysis here more reasonable.

关键词： Community detection limited resolution complex networks

来源：评论

学校读者我要写书评

暂无评论

A Weighted Parsimony Model for Community Detection in complex Networks

A Weighted Parsimony Model for Community Detection in Comple...

引用

第三届最优化与系统生物学国际研讨会

作者： Junhua Zhang Xiang-Sun Zhang Academy of Mathematics and Systems Science CAS Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems ScienceCAS

Many real-world networks have a common feature of organization,i.e.,community *** this structure is fundamental for uncovering the links between the structure and the function in complex networks and for practical applications in many disciplines such as biology and *** this paper we propose a weighted parsimony criterion for community detection in complex *** criterion relates communities with cliques(or complete subgraphs).Parsimony here means that as minimal as possible number of inserted and deleted edges is needed when we make the network considered become a disjoint union of cliques.A weight based on the topological features of the network is introduced to ensure the obtained subgraphs to be communities by balancing the inserted and deleted *** on real networks give excellent results.

关键词： Community detection parsimony cliques complex networks

来源：评论

学校读者我要写书评

暂无评论

A random Iterative Algorithm for Community Detection

A Random Iterative Algorithm for Community Detection

引用

第三届最优化与系统生物学国际研讨会

作者： Junhua Zhang Shihua Chen Academy of Mathematics and Systems Science CAS Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems ScienceCAS College of Mathematics and Statistics Wuhan University

Research on community structure detection in complex networks has attracted a great deal of attention in recent *** this paper we propose a random iterative algorithm to uncover meaningful *** algorithm starts with initial population *** individual of the population is encoded with the community identifiers of the nodes in the network,so it is a potential solution of the community structure of the network *** are randomly assigned into communities at the beginning of the *** each iteration some nodes are randomly selected,their community identifiers are reassigned according to the modularity function and the measure of information discrepancy based on the shortest path profiles of nodes in the *** the end,a proper community structure can be detected by the identifiers encoded in the individual with the largest *** algorithm does not need any prior knowledge about the number of communities and can give an appropriate number by maximizing the modularity *** computational results of the method on real-world networks confirm its capability.

关键词： Community detection random iteration complex networks

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：