This paper deeply discusses the characteristics of decorative language in China’s contemporary oil painting art,analyzes its performance in form,color,and composition,and expounds on the application of decorative lan...This paper deeply discusses the characteristics of decorative language in China’s contemporary oil painting art,analyzes its performance in form,color,and composition,and expounds on the application of decorative language in contemporary oil painting practice with specific artists’works.Through the study of this unique artistic language,this paper reveals the innovation and development of China’s contemporary oil painting in integrating traditional and modern,Eastern and Western artistic elements,and provides theoretical reference and practical enlightenment for the further development of China’s contemporary oil painting art.展开更多
We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dime...We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.展开更多
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the firs...We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the first step,we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace.By this space,we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the pressure.In the second step,we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space.We derive error estimates for all unknowns under both L 2 norms and energy norms.Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.展开更多
1 Introduction and main contributions The exploration of polarized communities,which consist of two antagonistic subgraphs and include a set of query nodes,is a crucial task in community search on signed networks.Most...1 Introduction and main contributions The exploration of polarized communities,which consist of two antagonistic subgraphs and include a set of query nodes,is a crucial task in community search on signed networks.Most existing methods either predominantly rely on topological structure while disregarding node attributes or tend to prioritize the global identification of all polarized communities.Thus,they fail to consider two crucial insights.Firstly,integrating node attributes with network structure can enhance the search quality for polarized communities in attributed signed networks by leveraging complementary information.Secondly,global criteria-based polarized community detection aims to identify all polarized communities,neglecting personalized analyses centered around individual users.展开更多
Community search is an important problem in network analysis,which has attracted much attention in recent years.As a query-oriented variant of community detection problem,community search starts with some given nodes,...Community search is an important problem in network analysis,which has attracted much attention in recent years.As a query-oriented variant of community detection problem,community search starts with some given nodes,pays more attention to local network structures,and gets personalized resultant communities quickly.The existing community search method typically returns a single target community containing query nodes by default.This is a strict requirement and does not allow much flexibility.In many realworld applications,however,query nodes are expected to be located in multiple communities with different semantics.To address this limitation of existing methods,an efficient spectral-based Multi-Scale Community Search method(MSCS)is proposed,which can simultaneously identify the multi-scale target local communities to which query node belong.In MSCS,each node is equipped with a graph Fourier multiplier operator.The access of the graph Fourier multiplier operator helps nodes to obtain feature representations at various community scales.In addition,an efficient algorithm is proposed for avoiding the large number of matrix operations due to spectral methods.Comprehensive experimental evaluations on a variety of real-world datasets demonstrate the effectiveness and efficiency of the proposed method.展开更多
1Introduction and main contributions Recently,community search over Heterogeneous Information Networks(HINs)has attracted much attention in graph analysis,which aims to search for local communities containing query no...1Introduction and main contributions Recently,community search over Heterogeneous Information Networks(HINs)has attracted much attention in graph analysis,which aims to search for local communities containing query node.Although existing community search studies in HINs have proved effective in converting heterogeneous graphs to homogeneous graphs via pre-defined meta-paths with consistent head and tail node types,two major limitations stilexist.First,they fail to properly utilize the intermediate nodes to assign weights on the edges of the induced homogeneous graph.展开更多
We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reco...We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials.This space allows us to solve the first-order system in two sequential steps.In the first step,we solve a nonlinear system to obtain the approximation to the gradient.A Newton iteration is adopted to handle the nonlinearity of the system.The approximation to the primitive variable is obtained from the approximate gradient by a trivial least squares finite element method in the second step.Numerical examples in both two and three dimensions are presented to show an optimal convergence rate in accuracy.It is interesting to observe that the approximation solution is piecewise convex.Particularly,with the reconstructed approximation space,the proposed method numerically demonstrates a remarkable robustness.The convergence of the Newton iteration does not rely on the initial values.The dependence of the convergence on the penalty parameter in the discretization is also negligible,in comparison to the classical discontinuous approximation space.展开更多
文摘This paper deeply discusses the characteristics of decorative language in China’s contemporary oil painting art,analyzes its performance in form,color,and composition,and expounds on the application of decorative language in contemporary oil painting practice with specific artists’works.Through the study of this unique artistic language,this paper reveals the innovation and development of China’s contemporary oil painting in integrating traditional and modern,Eastern and Western artistic elements,and provides theoretical reference and practical enlightenment for the further development of China’s contemporary oil painting art.
基金the National Natural Science Foundation of China for Distinguished Young Scholars 11425106National Natural Science Foundation of China Grants 91630313+1 种基金CAS NCMISthe National Natural Science Foundation of China Grants 91630313 and 11671312.
文摘We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.
基金supported by the Science Challenge Project(No.TZ2016002)the National Natural Science Foundation in China(No.11971041 and 11421101).
文摘We propose a new least squares finite element method to solve the Stokes problem with two sequential steps.The approximation spaces are constructed by the patch reconstruction with one unknown per element.For the first step,we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace.By this space,we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the pressure.In the second step,we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space.We derive error estimates for all unknowns under both L 2 norms and energy norms.Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.
基金supported by the Industrial Support Project of Gansu Colleges,China(No.2022CYZC11)the National Natural Science Foundation of China(Grant Nos.61762078,62276073 and U22A2099)the Guangxi Key Laboratory of Trusted Software(kx202302).
文摘1 Introduction and main contributions The exploration of polarized communities,which consist of two antagonistic subgraphs and include a set of query nodes,is a crucial task in community search on signed networks.Most existing methods either predominantly rely on topological structure while disregarding node attributes or tend to prioritize the global identification of all polarized communities.Thus,they fail to consider two crucial insights.Firstly,integrating node attributes with network structure can enhance the search quality for polarized communities in attributed signed networks by leveraging complementary information.Secondly,global criteria-based polarized community detection aims to identify all polarized communities,neglecting personalized analyses centered around individual users.
基金supported by the Industrial Support Project of Gansu Colleges(2022CYZC-11)National Natural Science Foundation of China(61363058,61966004)+1 种基金Northwest Normal University Young Teachers Research Capacity Promotion Play(NWNU-LKQN2019-2)Natural Science Foundation of Gansu Province(21JR7RA114).
文摘Community search is an important problem in network analysis,which has attracted much attention in recent years.As a query-oriented variant of community detection problem,community search starts with some given nodes,pays more attention to local network structures,and gets personalized resultant communities quickly.The existing community search method typically returns a single target community containing query nodes by default.This is a strict requirement and does not allow much flexibility.In many realworld applications,however,query nodes are expected to be located in multiple communities with different semantics.To address this limitation of existing methods,an efficient spectral-based Multi-Scale Community Search method(MSCS)is proposed,which can simultaneously identify the multi-scale target local communities to which query node belong.In MSCS,each node is equipped with a graph Fourier multiplier operator.The access of the graph Fourier multiplier operator helps nodes to obtain feature representations at various community scales.In addition,an efficient algorithm is proposed for avoiding the large number of matrix operations due to spectral methods.Comprehensive experimental evaluations on a variety of real-world datasets demonstrate the effectiveness and efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China(Grant Nos.61762078,61363058,61966004)Natural Science Foundation of Gansu(21JR7RA114)Northwest Normal University Young Teachers Research Capacity Promotion Plan(NWNULKQN2019-2).
文摘1Introduction and main contributions Recently,community search over Heterogeneous Information Networks(HINs)has attracted much attention in graph analysis,which aims to search for local communities containing query node.Although existing community search studies in HINs have proved effective in converting heterogeneous graphs to homogeneous graphs via pre-defined meta-paths with consistent head and tail node types,two major limitations stilexist.First,they fail to properly utilize the intermediate nodes to assign weights on the edges of the induced homogeneous graph.
基金This research was supported by the National Natural Science Foundation in China(Nos.12201442,and 11971041).
文摘We propose a numerical method to solve the Monge-Ampère equation which admits a classical convex solution.The Monge-Ampère equation is reformulated into an equivalent first-order system.We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials.This space allows us to solve the first-order system in two sequential steps.In the first step,we solve a nonlinear system to obtain the approximation to the gradient.A Newton iteration is adopted to handle the nonlinearity of the system.The approximation to the primitive variable is obtained from the approximate gradient by a trivial least squares finite element method in the second step.Numerical examples in both two and three dimensions are presented to show an optimal convergence rate in accuracy.It is interesting to observe that the approximation solution is piecewise convex.Particularly,with the reconstructed approximation space,the proposed method numerically demonstrates a remarkable robustness.The convergence of the Newton iteration does not rely on the initial values.The dependence of the convergence on the penalty parameter in the discretization is also negligible,in comparison to the classical discontinuous approximation space.
