In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of deg...In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of degree m,the initial values,and the exponents in absorption terms,we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time.Our current work extends the results achieved by Lin and Wu(Calc Var Partial Differ Equ,2017,56:Art 102)and Wu(Rev R Acad Cien Serie A Mat,2021,115:Art 133).展开更多
Using the linear space over the binary field that related to a graph G, a sufficient and necessary condition for the chromatic number of G is obtained.
This article is devoted to developing a deep learning method for the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computation...This article is devoted to developing a deep learning method for the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computationally numerical format has been used. In particular, for investigation mathematical models of the dynamical system of cancer cell invasion in inhomogeneous areas of human tissues have been considered. Neural operators were initially proposed to model the differential operator of PDEs. The GKNN mapping features between input data to the PDEs and their solutions have been constructed. The boundary integral method in combination with Green’s functions for a large number of boundary conditions is used. The tools applied in this development are based on the Fourier neural operators (FNOs), graph theory, theory elasticity, and singular integral equations.展开更多
无线光通信网络的隐蔽窃听攻击具有高度的隐蔽性和复杂性,其中包含的复杂数据模式和特征,加大了无线光通信网络隐蔽窃听攻击检测难度。故提出无线光通信网络隐蔽窃听攻击自适应检测研究。采用图信号处理方法全面监测无线光通信网络,捕...无线光通信网络的隐蔽窃听攻击具有高度的隐蔽性和复杂性,其中包含的复杂数据模式和特征,加大了无线光通信网络隐蔽窃听攻击检测难度。故提出无线光通信网络隐蔽窃听攻击自适应检测研究。采用图信号处理方法全面监测无线光通信网络,捕捉异常信号范围;利用人工智能技术识别隐蔽窃听攻击特征;建立基于混合核最小二乘支持向量机(hybridkernel least-squares support vector machine,HKLSSVM)的窃听攻击检测模型,通过引入混合核函数将数据映射到更高维的特征空间中,识别出的隐蔽窃听攻击特征,并通过鲸鱼提升算法选择最优的惩罚参数和内核参数,实现无线光通信网络隐蔽窃听攻击自适应检测。实验结果表明,所提方法能准确获取异常信号范围和异常信号,在保证计算稳定性的同时,提高攻击检测性能。展开更多
将压缩映射和同构映射引入核化图嵌入框架(kernel extension of graph embedding,简称KGE),从理论上证明了KGE框架内的各种核算法其实质是KPCA(kernel principal component analysis)+LGE(linear extension of graph embedding,简称LGE...将压缩映射和同构映射引入核化图嵌入框架(kernel extension of graph embedding,简称KGE),从理论上证明了KGE框架内的各种核算法其实质是KPCA(kernel principal component analysis)+LGE(linear extension of graph embedding,简称LGE)框架内的线性降维算法,并且基于所给出的理论框架提出了一种综合利用零空间和非零空间鉴别信息的组合方法.任何一种可以用核化图嵌入框架描述的核算法,都可以有相应的组合方法.在ORL,Yale,FERET和PIE人脸数据库上验证了所提出的理论和方法的有效性.展开更多
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LY21A010016)the National Natural Science Foundation of China(11901550).
文摘In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of degree m,the initial values,and the exponents in absorption terms,we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time.Our current work extends the results achieved by Lin and Wu(Calc Var Partial Differ Equ,2017,56:Art 102)and Wu(Rev R Acad Cien Serie A Mat,2021,115:Art 133).
文摘Using the linear space over the binary field that related to a graph G, a sufficient and necessary condition for the chromatic number of G is obtained.
文摘This article is devoted to developing a deep learning method for the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computationally numerical format has been used. In particular, for investigation mathematical models of the dynamical system of cancer cell invasion in inhomogeneous areas of human tissues have been considered. Neural operators were initially proposed to model the differential operator of PDEs. The GKNN mapping features between input data to the PDEs and their solutions have been constructed. The boundary integral method in combination with Green’s functions for a large number of boundary conditions is used. The tools applied in this development are based on the Fourier neural operators (FNOs), graph theory, theory elasticity, and singular integral equations.
文摘无线光通信网络的隐蔽窃听攻击具有高度的隐蔽性和复杂性,其中包含的复杂数据模式和特征,加大了无线光通信网络隐蔽窃听攻击检测难度。故提出无线光通信网络隐蔽窃听攻击自适应检测研究。采用图信号处理方法全面监测无线光通信网络,捕捉异常信号范围;利用人工智能技术识别隐蔽窃听攻击特征;建立基于混合核最小二乘支持向量机(hybridkernel least-squares support vector machine,HKLSSVM)的窃听攻击检测模型,通过引入混合核函数将数据映射到更高维的特征空间中,识别出的隐蔽窃听攻击特征,并通过鲸鱼提升算法选择最优的惩罚参数和内核参数,实现无线光通信网络隐蔽窃听攻击自适应检测。实验结果表明,所提方法能准确获取异常信号范围和异常信号,在保证计算稳定性的同时,提高攻击检测性能。
文摘将压缩映射和同构映射引入核化图嵌入框架(kernel extension of graph embedding,简称KGE),从理论上证明了KGE框架内的各种核算法其实质是KPCA(kernel principal component analysis)+LGE(linear extension of graph embedding,简称LGE)框架内的线性降维算法,并且基于所给出的理论框架提出了一种综合利用零空间和非零空间鉴别信息的组合方法.任何一种可以用核化图嵌入框架描述的核算法,都可以有相应的组合方法.在ORL,Yale,FERET和PIE人脸数据库上验证了所提出的理论和方法的有效性.
