The numerical manifold method （NMM） can calculate the movements and deformations of structures or materials. Both the finite element method （FEM） for continua and the discontinuous deformation analysis （DDA） for...The numerical manifold method （NMM） can calculate the movements and deformations of structures or materials. Both the finite element method （FEM） for continua and the discontinuous deformation analysis （DDA） for block systems are special cases of NMM. NMM has separate mathematical covers and physical meshes： the mathematical covers define only fine or rough approximations; as the real material boundary, the physical mesh defines the integration fields. The mathematical covers are triangle units; the physical mesh includes the fault boundaries, joints, blocks and interfaces of different crust zones on the basis of a geological tectonic background. Aiming at the complex problem of continuous and discontinuous deformation across the Chinese continent, the numerical manifold method （NMM） is brought in to study crustal movement of the Stchuan-Yunnan area. Based on the GPS velocity field in the Sichuan-Yunnan area, a crustal strain and stress field is simulated and analyzed. Moreover, results show that the NMM is a more suitable method than DDA in simulating the movement of the Sichuan-Yunnan area. Finally, a kind of mechanism of crustal motion in the Sichuan-Yunnan area is discussed in the paper.展开更多
In this paper,for any local area-minimizing closed hypersurface∑with RcΣ=RΣ/ngΣ,immersed in a(n+1)-dimension Riemannian manifold M which has positive scalar curvature and nonnegative Ricci curvature,we obtain an u...In this paper,for any local area-minimizing closed hypersurface∑with RcΣ=RΣ/ngΣ,immersed in a(n+1)-dimension Riemannian manifold M which has positive scalar curvature and nonnegative Ricci curvature,we obtain an upper bound for the area of∑.In particular,when∑saturates the corresponding upper bound,∑is isometric to S^(n)and M splits in a neighborhood of∑.At the end of the paper,we also give the global version of this result.展开更多
In this paper, a new -graph regularized semi-supervised manifold learning （LRSML） method is proposed for indoor localization. Due to noise corruption and non-linearity of received signal strength （RSS）, traditiona...In this paper, a new -graph regularized semi-supervised manifold learning （LRSML） method is proposed for indoor localization. Due to noise corruption and non-linearity of received signal strength （RSS）, traditional approaches always fail to deliver accurate positioning results. The -graph is constructed by sparse representation of each sample with respect to remaining samples. Noise factor is considered in the construction process of -graph, leading to more robustness compared to traditional k-nearest-neighbor graph （KNN-graph）. The KNN-graph construction is supervised, while the -graph is assumed to be unsupervised without harnessing any data label information and uncovers the underlying sparse relationship of each data. Combining KNN-graph and -graph, both labeled and unlabeled information are utilized, so the LRSML method has the potential to convey more discriminative information compared to conventional methods. To overcome the non-linearity of RSS, kernel-based manifold learning method （K-LRSML） is employed through mapping the original signal data to a higher dimension Hilbert space. The efficiency and superiority of LRSML over current state of art methods are verified with extensive experiments on real data.展开更多
基金Supported by the National Natural Science Foundation of China （N0.40574006, N0.40344023）, DGLIGG （L04-02）.
文摘The numerical manifold method （NMM） can calculate the movements and deformations of structures or materials. Both the finite element method （FEM） for continua and the discontinuous deformation analysis （DDA） for block systems are special cases of NMM. NMM has separate mathematical covers and physical meshes： the mathematical covers define only fine or rough approximations; as the real material boundary, the physical mesh defines the integration fields. The mathematical covers are triangle units; the physical mesh includes the fault boundaries, joints, blocks and interfaces of different crust zones on the basis of a geological tectonic background. Aiming at the complex problem of continuous and discontinuous deformation across the Chinese continent, the numerical manifold method （NMM） is brought in to study crustal movement of the Stchuan-Yunnan area. Based on the GPS velocity field in the Sichuan-Yunnan area, a crustal strain and stress field is simulated and analyzed. Moreover, results show that the NMM is a more suitable method than DDA in simulating the movement of the Sichuan-Yunnan area. Finally, a kind of mechanism of crustal motion in the Sichuan-Yunnan area is discussed in the paper.
基金supported by National Science Foundation of China(11601467).
文摘In this paper,for any local area-minimizing closed hypersurface∑with RcΣ=RΣ/ngΣ,immersed in a(n+1)-dimension Riemannian manifold M which has positive scalar curvature and nonnegative Ricci curvature,we obtain an upper bound for the area of∑.In particular,when∑saturates the corresponding upper bound,∑is isometric to S^(n)and M splits in a neighborhood of∑.At the end of the paper,we also give the global version of this result.
基金supported by the Hi-Tech Research and Development Program of China(2009AA12Z324)
文摘In this paper, a new -graph regularized semi-supervised manifold learning （LRSML） method is proposed for indoor localization. Due to noise corruption and non-linearity of received signal strength （RSS）, traditional approaches always fail to deliver accurate positioning results. The -graph is constructed by sparse representation of each sample with respect to remaining samples. Noise factor is considered in the construction process of -graph, leading to more robustness compared to traditional k-nearest-neighbor graph （KNN-graph）. The KNN-graph construction is supervised, while the -graph is assumed to be unsupervised without harnessing any data label information and uncovers the underlying sparse relationship of each data. Combining KNN-graph and -graph, both labeled and unlabeled information are utilized, so the LRSML method has the potential to convey more discriminative information compared to conventional methods. To overcome the non-linearity of RSS, kernel-based manifold learning method （K-LRSML） is employed through mapping the original signal data to a higher dimension Hilbert space. The efficiency and superiority of LRSML over current state of art methods are verified with extensive experiments on real data.
