This article aims to identify the partial topological structures of delayed complex network.Based on the drive-response concept,a more universal model,which includes nonlinear couplings,stochastic perturbations and mu...This article aims to identify the partial topological structures of delayed complex network.Based on the drive-response concept,a more universal model,which includes nonlinear couplings,stochastic perturbations and multi-weights,is considered into drive-response networks.Different from previous methods,we obtain identification criteria by combining graph-theoretic method and adaptive synchronization.After that,the partial topological structures of stochastic multi-weighted complex networks with or without time delays can be identified successfully.Moreover,response network can reach synchronization with drive network.Ultimately,the effectiveness of the proposed theoretical results is validated through numerical simulations.展开更多
Generally,the distributed bundle adjustment(DBA)method uses multiple worker nodes to solve the bundle adjustment problems and overcomes the computation and memory storage limitations of a single computer.However,the p...Generally,the distributed bundle adjustment(DBA)method uses multiple worker nodes to solve the bundle adjustment problems and overcomes the computation and memory storage limitations of a single computer.However,the performance considerably degrades owing to the overhead introduced by the additional block partitioning step and synchronous waiting.Therefore,we propose a low-overhead consensus framework.A partial barrier based asynchronous method is proposed to early achieve consensus with respect to the faster worker nodes to avoid waiting for the slower ones.A scene summarization procedure is designed and integrated into the block partitioning step to ensure that clustering can be performed on the small summarized scene.Experiments conducted on public datasets show that our method can improve the worker node utilization rate and reduce the block partitioning time.Also,sample applications are demonstrated using our large-scale culture heritage datasets.展开更多
In the study of(partial)difference sets and their generalizations in groups G,the most widely used method is to translate their definition into an equation over group ring Z[G]and to investigate this equation by apply...In the study of(partial)difference sets and their generalizations in groups G,the most widely used method is to translate their definition into an equation over group ring Z[G]and to investigate this equation by applying complex representations of G.In this paper,we investigate the existence of(partial)difference sets in a different way.We project the group ring equations in Z[G]to Z[N]where N is a quotient group of G isomorphic to the additive group of a finite field,and then use polynomials over this finite field to derive some existence conditions.展开更多
Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectra...Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectral clustering, and kernel methods for machine learning. The more challenging problems are when a large number of eigenpairs or singular triplets need to be computed. We develop practical and efficient algorithms for these challenging problems. Our algorithms are based on a filter-accelerated block Davidson method.Two types of filters are utilized, one is Chebyshev polynomial filtering, the other is rational-function filtering by solving linear equations. The former utilizes the fastest growth of the Chebyshev polynomial among same degree polynomials; the latter employs the traditional idea of shift-invert, for which we address the important issue of automatic choice of shifts and propose a practical method for solving the shifted linear equations inside the block Davidson method. Our two filters can efficiently generate high-quality basis vectors to augment the projection subspace at each Davidson iteration step, which allows a restart scheme using an active projection subspace of small dimension. This makes our algorithms memory-economical, thus practical for large PEVD/PSVD calculations. We compare our algorithms with representative methods, including ARPACK, PROPACK, the randomized SVD method, and the limited memory SVD method. Extensive numerical tests on representative datasets demonstrate that, in general, our methods have similar or faster convergence speed in terms of CPU time, while requiring much lower memory comparing with other methods. The much lower memory requirement makes our methods more practical for large-scale PEVD/PSVD computations.展开更多
Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric di...Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.展开更多
基金supported by the National Natural Science Foundation of China(No.11601445)the Fundamental Research Funds for the Central Universities(No.2682020ZT109)the Central Governments Funds for Guiding Local Scientific and Technological Development(No.2021ZYD0010).
文摘This article aims to identify the partial topological structures of delayed complex network.Based on the drive-response concept,a more universal model,which includes nonlinear couplings,stochastic perturbations and multi-weights,is considered into drive-response networks.Different from previous methods,we obtain identification criteria by combining graph-theoretic method and adaptive synchronization.After that,the partial topological structures of stochastic multi-weighted complex networks with or without time delays can be identified successfully.Moreover,response network can reach synchronization with drive network.Ultimately,the effectiveness of the proposed theoretical results is validated through numerical simulations.
基金Project supported by the Key R&D Program of Zhejiang Province,China(No.2018C03051)the Key Scientific Research Base for Digital Conservation of Cave Temples of the National Cultural Heritage Administration,China。
文摘Generally,the distributed bundle adjustment(DBA)method uses multiple worker nodes to solve the bundle adjustment problems and overcomes the computation and memory storage limitations of a single computer.However,the performance considerably degrades owing to the overhead introduced by the additional block partitioning step and synchronous waiting.Therefore,we propose a low-overhead consensus framework.A partial barrier based asynchronous method is proposed to early achieve consensus with respect to the faster worker nodes to avoid waiting for the slower ones.A scene summarization procedure is designed and integrated into the block partitioning step to ensure that clustering can be performed on the small summarized scene.Experiments conducted on public datasets show that our method can improve the worker node utilization rate and reduce the block partitioning time.Also,sample applications are demonstrated using our large-scale culture heritage datasets.
基金This work is partially supported by Natural Science Foundation of Hunan Province(No.2019JJ30030)Training Program for Excellent Young Innovators of Changsha(No.kql905052).
文摘In the study of(partial)difference sets and their generalizations in groups G,the most widely used method is to translate their definition into an equation over group ring Z[G]and to investigate this equation by applying complex representations of G.In this paper,we investigate the existence of(partial)difference sets in a different way.We project the group ring equations in Z[G]to Z[N]where N is a quotient group of G isomorphic to the additive group of a finite field,and then use polynomials over this finite field to derive some existence conditions.
基金supported by National Science Foundation of USA (Grant Nos. DMS1228271 and DMS-1522587)National Natural Science Foundation of China for Creative Research Groups (Grant No. 11321061)+1 种基金the National Basic Research Program of China (Grant No. 2011CB309703)the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
文摘Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectral clustering, and kernel methods for machine learning. The more challenging problems are when a large number of eigenpairs or singular triplets need to be computed. We develop practical and efficient algorithms for these challenging problems. Our algorithms are based on a filter-accelerated block Davidson method.Two types of filters are utilized, one is Chebyshev polynomial filtering, the other is rational-function filtering by solving linear equations. The former utilizes the fastest growth of the Chebyshev polynomial among same degree polynomials; the latter employs the traditional idea of shift-invert, for which we address the important issue of automatic choice of shifts and propose a practical method for solving the shifted linear equations inside the block Davidson method. Our two filters can efficiently generate high-quality basis vectors to augment the projection subspace at each Davidson iteration step, which allows a restart scheme using an active projection subspace of small dimension. This makes our algorithms memory-economical, thus practical for large PEVD/PSVD calculations. We compare our algorithms with representative methods, including ARPACK, PROPACK, the randomized SVD method, and the limited memory SVD method. Extensive numerical tests on representative datasets demonstrate that, in general, our methods have similar or faster convergence speed in terms of CPU time, while requiring much lower memory comparing with other methods. The much lower memory requirement makes our methods more practical for large-scale PEVD/PSVD computations.
文摘Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.
