In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator...In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.展开更多
A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schm...A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.展开更多
现有异质图(Heterogeneous Graph,HG)表示方法大都基于强大的图神经网络,聚合元路径内及元路径之间的语义信息来嵌入节点。然而,现有方法忽视了HG中节点的异质性,导致邻居节点中的无关信息沿着复杂结构扩散到高阶节点,扰动HG表示。为克...现有异质图(Heterogeneous Graph,HG)表示方法大都基于强大的图神经网络,聚合元路径内及元路径之间的语义信息来嵌入节点。然而,现有方法忽视了HG中节点的异质性,导致邻居节点中的无关信息沿着复杂结构扩散到高阶节点,扰动HG表示。为克服该问题,本文提出一种标签独立信息压缩的异质图表示方法LICHGR(Label-independent Information Compression for Heterogeneous Graph Representation)。LICHGR的核心思想是在信息瓶颈的指导下,利用希尔伯特-斯密特独立性准则限制异质图中标签独立信息的传播而尽可能保留标签依赖的信息。具体地,LICHGR通过在输入特征、元路径内隐藏特征、真实标签之间构造多方面的标签独立信息压缩限制,抽取丰富的标签依赖的信息,从而提高异质图表示质量。在3个公开的数据集上设计的多个实验充分验证了LICHGR的有效性。展开更多
基金Supported by National Natural Science Foundation of China(10171035)Natural Science Foundation of Gansu Province(ZS021-A25-004-Z) NWNU-KJCXGC-212
文摘In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
基金supported by the National Nature Science Foundation of China (Grant Nos.12031002,11971086)supported by the Dalian High-Level Talent Innovation Project (Grant No.2020RD09).
文摘A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.
文摘现有异质图(Heterogeneous Graph,HG)表示方法大都基于强大的图神经网络,聚合元路径内及元路径之间的语义信息来嵌入节点。然而,现有方法忽视了HG中节点的异质性,导致邻居节点中的无关信息沿着复杂结构扩散到高阶节点,扰动HG表示。为克服该问题,本文提出一种标签独立信息压缩的异质图表示方法LICHGR(Label-independent Information Compression for Heterogeneous Graph Representation)。LICHGR的核心思想是在信息瓶颈的指导下,利用希尔伯特-斯密特独立性准则限制异质图中标签独立信息的传播而尽可能保留标签依赖的信息。具体地,LICHGR通过在输入特征、元路径内隐藏特征、真实标签之间构造多方面的标签独立信息压缩限制,抽取丰富的标签依赖的信息,从而提高异质图表示质量。在3个公开的数据集上设计的多个实验充分验证了LICHGR的有效性。
