Practical real-world scenarios such as the Internet,social networks,and biological networks present the challenges of data scarcity and complex correlations,which limit the applications of artificial intelligence.The ...Practical real-world scenarios such as the Internet,social networks,and biological networks present the challenges of data scarcity and complex correlations,which limit the applications of artificial intelligence.The graph structure is a typical tool used to formulate such correlations,it is incapable of modeling highorder correlations among different objects in systems;thus,the graph structure cannot fully convey the intricate correlations among objects.Confronted with the aforementioned two challenges,hypergraph computation models high-order correlations among data,knowledge,and rules through hyperedges and leverages these high-order correlations to enhance the data.Additionally,hypergraph computation achieves collaborative computation using data and high-order correlations,thereby offering greater modeling flexibility.In particular,we introduce three types of hypergraph computation methods:①hypergraph structure modeling,②hypergraph semantic computing,and③efficient hypergraph computing.We then specify how to adopt hypergraph computation in practice by focusing on specific tasks such as three-dimensional(3D)object recognition,revealing that hypergraph computation can reduce the data requirement by 80%while achieving comparable performance or improve the performance by 52%given the same data,compared with a traditional data-based method.A comprehensive overview of the applications of hypergraph computation in diverse domains,such as intelligent medicine and computer vision,is also provided.Finally,we introduce an open-source deep learning library,DeepHypergraph(DHG),which can serve as a tool for the practical usage of hypergraph computation.展开更多
近年来,利用高阶交互信息进行多层网络社区检测已成为复杂网络分析领域的研究热点。尽管多层网络社区检测的研究已取得了一些进展,但大多数方法忽略了网络各层之间的联系。为了解决这一问题,提出了一种模体(motif)感知的自适应跨层游走...近年来,利用高阶交互信息进行多层网络社区检测已成为复杂网络分析领域的研究热点。尽管多层网络社区检测的研究已取得了一些进展,但大多数方法忽略了网络各层之间的联系。为了解决这一问题,提出了一种模体(motif)感知的自适应跨层游走社区检测算法(Motif-aware Adaptive Cross-Layer random walk Community Detection,MACLCD)。该算法充分考虑了多层网络各层内的高阶交互特性以及层间的相关性,有效整合了多层网络的结构信息,提高了社区检测结果的准确性。具体地,首先从网络和节点的角度进行综合度量,揭示网络层间相关性;其次,考虑了各层网络可能具有不同的局部和全局结构特征,利用motif识别各层网络特有的高阶交互结构,构建多层加权混合阶网络;进一步,设计了多层网络跨层游走模型,并引入跳转因子,以确保随机游走能够自适应地遍历多层网络,从而捕获更丰富的网络结构信息。在4个真实的网络数据集上进行实验比较分析,结果表明MACLCD算法在社区检测方面性能较优,相比目前表现最佳的对比算法在ACC和NMI上分别提高了10%和8.9%。展开更多
The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schem...The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.展开更多
Identifying important nodes and edges in complex networks has always been a popular research topic in network science and also has important implications for the protection of real-world complex systems.Finding the cr...Identifying important nodes and edges in complex networks has always been a popular research topic in network science and also has important implications for the protection of real-world complex systems.Finding the critical structures in a system allows us to protect the system from attacks or failures with minimal cost.To date,the problem of identifying critical nodes in networks has been widely studied by many scholars,and the theory is becoming increasingly mature.However,there is relatively little research related to edges.In fact,critical edges play an important role in maintaining the basic functions of the network and keeping the integrity of the structure.Sometimes protecting critical edges is less costly and more flexible in operation than just focusing on nodes.Considering the integrity of the network topology and the propagation dynamics on it,this paper proposes a centrality measure based on the number of high-order structural overlaps in the first and second-order neighborhoods of edges.The effectiveness of the metric is verified by the infection-susceptibility(SI)model,the robustness index R,and the number of connected branchesθ.A comparison is made with three currently popular edge importance metrics from two synthetic and four real networks.The simulation results show that the method outperforms existing methods in identifying critical edges that have a significant impact on both network connectivity and propagation dynamics.At the same time,the near-linear time complexity can be applied to large-scale networks.展开更多
The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scal...The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.展开更多
According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (no...According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (non-oscillatory, containing no free parameters, and dissipative scheme) scheme. It was applied in solving linear-wave equation, 1D Euler equations and 3D Navier-Stokes equations. The numerical results indicate that the WNND scheme which does not increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme. Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°, the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating, which occurs from the combined-point (which consists of saddle and node points). The separating area of upper wing surface is increasing with the (AoA's) increasing. The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with Zhang Hanxin's theory. Additionally, the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.展开更多
文摘Practical real-world scenarios such as the Internet,social networks,and biological networks present the challenges of data scarcity and complex correlations,which limit the applications of artificial intelligence.The graph structure is a typical tool used to formulate such correlations,it is incapable of modeling highorder correlations among different objects in systems;thus,the graph structure cannot fully convey the intricate correlations among objects.Confronted with the aforementioned two challenges,hypergraph computation models high-order correlations among data,knowledge,and rules through hyperedges and leverages these high-order correlations to enhance the data.Additionally,hypergraph computation achieves collaborative computation using data and high-order correlations,thereby offering greater modeling flexibility.In particular,we introduce three types of hypergraph computation methods:①hypergraph structure modeling,②hypergraph semantic computing,and③efficient hypergraph computing.We then specify how to adopt hypergraph computation in practice by focusing on specific tasks such as three-dimensional(3D)object recognition,revealing that hypergraph computation can reduce the data requirement by 80%while achieving comparable performance or improve the performance by 52%given the same data,compared with a traditional data-based method.A comprehensive overview of the applications of hypergraph computation in diverse domains,such as intelligent medicine and computer vision,is also provided.Finally,we introduce an open-source deep learning library,DeepHypergraph(DHG),which can serve as a tool for the practical usage of hypergraph computation.
文摘近年来,利用高阶交互信息进行多层网络社区检测已成为复杂网络分析领域的研究热点。尽管多层网络社区检测的研究已取得了一些进展,但大多数方法忽略了网络各层之间的联系。为了解决这一问题,提出了一种模体(motif)感知的自适应跨层游走社区检测算法(Motif-aware Adaptive Cross-Layer random walk Community Detection,MACLCD)。该算法充分考虑了多层网络各层内的高阶交互特性以及层间的相关性,有效整合了多层网络的结构信息,提高了社区检测结果的准确性。具体地,首先从网络和节点的角度进行综合度量,揭示网络层间相关性;其次,考虑了各层网络可能具有不同的局部和全局结构特征,利用motif识别各层网络特有的高阶交互结构,构建多层加权混合阶网络;进一步,设计了多层网络跨层游走模型,并引入跳转因子,以确保随机游走能够自适应地遍历多层网络,从而捕获更丰富的网络结构信息。在4个真实的网络数据集上进行实验比较分析,结果表明MACLCD算法在社区检测方面性能较优,相比目前表现最佳的对比算法在ACC和NMI上分别提高了10%和8.9%。
基金Project supported by the National Natural Science Foundation of China and the National Key Project for Basic Research.
文摘The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.
文摘Identifying important nodes and edges in complex networks has always been a popular research topic in network science and also has important implications for the protection of real-world complex systems.Finding the critical structures in a system allows us to protect the system from attacks or failures with minimal cost.To date,the problem of identifying critical nodes in networks has been widely studied by many scholars,and the theory is becoming increasingly mature.However,there is relatively little research related to edges.In fact,critical edges play an important role in maintaining the basic functions of the network and keeping the integrity of the structure.Sometimes protecting critical edges is less costly and more flexible in operation than just focusing on nodes.Considering the integrity of the network topology and the propagation dynamics on it,this paper proposes a centrality measure based on the number of high-order structural overlaps in the first and second-order neighborhoods of edges.The effectiveness of the metric is verified by the infection-susceptibility(SI)model,the robustness index R,and the number of connected branchesθ.A comparison is made with three currently popular edge importance metrics from two synthetic and four real networks.The simulation results show that the method outperforms existing methods in identifying critical edges that have a significant impact on both network connectivity and propagation dynamics.At the same time,the near-linear time complexity can be applied to large-scale networks.
基金Project supported by the Science Challenge Program(No.TZ2016001)the National Natural Science Foundation of China(Nos.11472277,11572331,11232011,and 11772337)+2 种基金the Strategic Priority Research Program,Chinese Academy of Sciences(CAS)(No.XDB22040104)the Key Research Program of Frontier Sciences,CAS(No.QYZDJ-SSW-SYS002)the National Basic Research Program of China(973 Program)(No.2013CB834100)
文摘The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.
文摘According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (non-oscillatory, containing no free parameters, and dissipative scheme) scheme. It was applied in solving linear-wave equation, 1D Euler equations and 3D Navier-Stokes equations. The numerical results indicate that the WNND scheme which does not increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme. Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°, the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating, which occurs from the combined-point (which consists of saddle and node points). The separating area of upper wing surface is increasing with the (AoA's) increasing. The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with Zhang Hanxin's theory. Additionally, the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.
