This paper presents two new theorems for multiplicative perturbations of C-regularized resolvent families, which generalize the previous related ones for the resolvent families.
在复杂网络分析中,挖掘社区结构是一个重要且具有挑战性的研究方向。现有的基于深度学习方法在图相关任务中取得了不错的效果,但鲜有处理社区检测任务,尤其是重叠社区检测,并且也未能充分挖掘和利用网络的拓扑结构信息。为此,提出了一...在复杂网络分析中,挖掘社区结构是一个重要且具有挑战性的研究方向。现有的基于深度学习方法在图相关任务中取得了不错的效果,但鲜有处理社区检测任务,尤其是重叠社区检测,并且也未能充分挖掘和利用网络的拓扑结构信息。为此,提出了一种图正则化模糊自动编码器的重叠社区检测方法(Overlapping Community Detection with Graph Regularized Fuzzy AutoEncoder,FAE)。首先,运用自动编码器将网络拓扑编码为低维表示,进一步通过模糊C均值聚类形成模糊隶属度矩阵,随后解码模糊隶属度矩阵以重构网络拓扑。然后,将用于刻画网络中结构信息的图正则融入上述自动编码器。再者,融合后的自动编码器构成堆叠自动编码器,以获取深度模糊隶属度矩阵。最后,基于模糊集理论,使用深度模糊隶属度矩阵划分重叠社区。在3组人工网络和6个真实网络上的实验结果表明,该方法基于重叠标准互信息熵(ONMI)、杰卡德指数(Jaccard)、F1分数(F1-Score)的评估性能优于7种经典算法的大部分算法,展示了其在处理复杂网络重叠社区检测问题上的潜力。展开更多
Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all po...Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.展开更多
文摘This paper presents two new theorems for multiplicative perturbations of C-regularized resolvent families, which generalize the previous related ones for the resolvent families.
文摘在复杂网络分析中,挖掘社区结构是一个重要且具有挑战性的研究方向。现有的基于深度学习方法在图相关任务中取得了不错的效果,但鲜有处理社区检测任务,尤其是重叠社区检测,并且也未能充分挖掘和利用网络的拓扑结构信息。为此,提出了一种图正则化模糊自动编码器的重叠社区检测方法(Overlapping Community Detection with Graph Regularized Fuzzy AutoEncoder,FAE)。首先,运用自动编码器将网络拓扑编码为低维表示,进一步通过模糊C均值聚类形成模糊隶属度矩阵,随后解码模糊隶属度矩阵以重构网络拓扑。然后,将用于刻画网络中结构信息的图正则融入上述自动编码器。再者,融合后的自动编码器构成堆叠自动编码器,以获取深度模糊隶属度矩阵。最后,基于模糊集理论,使用深度模糊隶属度矩阵划分重叠社区。在3组人工网络和6个真实网络上的实验结果表明,该方法基于重叠标准互信息熵(ONMI)、杰卡德指数(Jaccard)、F1分数(F1-Score)的评估性能优于7种经典算法的大部分算法,展示了其在处理复杂网络重叠社区检测问题上的潜力。
基金supported by the NSF of Chinasupported by TRAPOYT and the NSF of China(No.10371046)
文摘Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.
