This review summarizes the development of particle-based numerical manifold method(PNMM)and its applications to rock dynamics.The fundamental principle of numerical manifold method(NMM)is first briefly introduced.Then...This review summarizes the development of particle-based numerical manifold method(PNMM)and its applications to rock dynamics.The fundamental principle of numerical manifold method(NMM)is first briefly introduced.Then,the history of the newly developed PNMM is given.Basic idea of PNMM and its simulation procedure are presented.Considering that PNMM could be regarded as an NMM-based model,a comparison of PNMM and NMM is discussed from several points of view in this paper.Besides,accomplished applications of PNMM to the dynamic rock fracturing are also reviewed.Finally,some recommendations are provided for the future work of PNMM.展开更多
We consider base spaces of Lagrangian fibrations from singular symplectic varieties.After defining cohomologically irreducible symplectic varieties,we construct an example of Lagrangian fibration whose base space is i...We consider base spaces of Lagrangian fibrations from singular symplectic varieties.After defining cohomologically irreducible symplectic varieties,we construct an example of Lagrangian fibration whose base space is isomorphic to a quotient of the projective space.We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.展开更多
A new framework for free-surface design is proposed.Using Manifolds can generalize the spline scheme to surfaces of arbitrary topology,Physics-based modeling incorporate physical laws into shape representation to prov...A new framework for free-surface design is proposed.Using Manifolds can generalize the spline scheme to surfaces of arbitrary topology,Physics-based modeling incorporate physical laws into shape representation to provide direct shape interaction.The combination presents a new method inherits the attractive properties of the manifold surface as well as that of the physcis-based models.展开更多
Latent Semantic Analysis involves natural language processing techniques for analyzing relationships between a set of documents and the terms they contain, by producing a set of concepts (related to the documents and ...Latent Semantic Analysis involves natural language processing techniques for analyzing relationships between a set of documents and the terms they contain, by producing a set of concepts (related to the documents and terms) called semantic topics. These semantic topics assist search engine users by providing leads to the more relevant document. We develope a novel algorithm called Latent Semantic Manifold (LSM) that can identify the semantic topics in the high-dimensional web data. The LSM algorithm is established upon the concepts of topology and probability. Asearch tool is also developed using the LSM algorithm. This search tool is deployed for two years at two sites in Taiwan: 1) Taipei Medical University Library, Taipei, and 2) Biomedical Engineering Laboratory, Institute of Biomedical Engineering, National Taiwan University, Taipei. We evaluate the effectiveness and efficiency of the LSM algorithm by comparing with other contemporary algorithms. The results show that the LSM algorithm outperforms compared with others. This algorithm can be used to enhance the functionality of currently available search engines.展开更多
认识染色体的三维空间结构对于理解细胞核内基因组的表达、调控等具有重要作用.针对Hi-C数据稀疏和含有噪声的特点,提出了基于流形优化(manifold based optimization,MBO)与参数优化相结合的染色体三维结构预测方法——变参数的基于流...认识染色体的三维空间结构对于理解细胞核内基因组的表达、调控等具有重要作用.针对Hi-C数据稀疏和含有噪声的特点,提出了基于流形优化(manifold based optimization,MBO)与参数优化相结合的染色体三维结构预测方法——变参数的基于流形优化的算法(variable-parameter MBO,VMBO).通过黄金分割算法迭代优化转换参数,将染色体片段间的接触频率转换为空间距离值;然后用MBO算法重构染色体的三维平均结构(consensus structures).在实验部分用模拟数据集和真实的Hi-C数据集进行三维结构预测,预测结果的均方根误差(root mean squared deviation,RMSD)和距离的斯皮尔曼相关系数(distance Spearman correlation coefficient,d SCC)说明了VMBO算法的有效性和鲁棒性.展开更多
基金the financial support to the development of PNMM from the Laboratory of Rock Mechanics at école Polytechnique Fédérale de Lausanne (LMR-EPFL), Monash Universitythe National Natural Science Foundation of China (Grant No. 11802058)
文摘This review summarizes the development of particle-based numerical manifold method(PNMM)and its applications to rock dynamics.The fundamental principle of numerical manifold method(NMM)is first briefly introduced.Then,the history of the newly developed PNMM is given.Basic idea of PNMM and its simulation procedure are presented.Considering that PNMM could be regarded as an NMM-based model,a comparison of PNMM and NMM is discussed from several points of view in this paper.Besides,accomplished applications of PNMM to the dynamic rock fracturing are also reviewed.Finally,some recommendations are provided for the future work of PNMM.
基金supported by Japan Society for Promotion of Sciences(Grant No.18684001)
文摘We consider base spaces of Lagrangian fibrations from singular symplectic varieties.After defining cohomologically irreducible symplectic varieties,we construct an example of Lagrangian fibration whose base space is isomorphic to a quotient of the projective space.We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.
基金Funded by the Chinese National Natural Science Foundation (No.50105013).
文摘A new framework for free-surface design is proposed.Using Manifolds can generalize the spline scheme to surfaces of arbitrary topology,Physics-based modeling incorporate physical laws into shape representation to provide direct shape interaction.The combination presents a new method inherits the attractive properties of the manifold surface as well as that of the physcis-based models.
文摘Latent Semantic Analysis involves natural language processing techniques for analyzing relationships between a set of documents and the terms they contain, by producing a set of concepts (related to the documents and terms) called semantic topics. These semantic topics assist search engine users by providing leads to the more relevant document. We develope a novel algorithm called Latent Semantic Manifold (LSM) that can identify the semantic topics in the high-dimensional web data. The LSM algorithm is established upon the concepts of topology and probability. Asearch tool is also developed using the LSM algorithm. This search tool is deployed for two years at two sites in Taiwan: 1) Taipei Medical University Library, Taipei, and 2) Biomedical Engineering Laboratory, Institute of Biomedical Engineering, National Taiwan University, Taipei. We evaluate the effectiveness and efficiency of the LSM algorithm by comparing with other contemporary algorithms. The results show that the LSM algorithm outperforms compared with others. This algorithm can be used to enhance the functionality of currently available search engines.
