In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize th...In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of Circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.展开更多
This article proposes a simultaneous localization and mapping(SLAM) version with continuous probabilistic mapping(CPSLAM), i.e., an algorithm of simultaneous localization and mapping that avoids the use of grids, and ...This article proposes a simultaneous localization and mapping(SLAM) version with continuous probabilistic mapping(CPSLAM), i.e., an algorithm of simultaneous localization and mapping that avoids the use of grids, and thus, does not require a discretized environment. A Markov random field(MRF) is considered to model this SLAM version with high spatial resolution maps. The mapping methodology is based on a point cloud generated by successive observations of the environment, which is kept bounded and representative by including a novel recursive subsampling method. The CP-SLAM problem is solved via iterated conditional modes(ICM), which is a classic algorithm with theoretical convergence over any MRF. The probabilistic maps are the most appropriate to represent dynamic environments, and can be easily implemented in other versions of the SLAM problem, such as the multi-robot version. Simulations and real experiments show the flexibility and excellent performance of this proposal.展开更多
The number of modes (also known as modality) of a kernel density estimator (KDE) draws lots of interests and is important in practice. In this paper, we develop an inference framework on the modality of a KDE under mu...The number of modes (also known as modality) of a kernel density estimator (KDE) draws lots of interests and is important in practice. In this paper, we develop an inference framework on the modality of a KDE under multivariate setting using Gaussian kernel. We applied the modal clustering method proposed by [1] for mode hunting. A test statistic and its asymptotic distribution are derived to assess the significance of each mode. The inference procedure is applied on both simulated and real data sets.展开更多
Modalclust is an R package which performs Hierarchical Mode Association Clustering (HMAC) along with its parallel implementation over several processors. Modal clustering techniques are especially designed to efficien...Modalclust is an R package which performs Hierarchical Mode Association Clustering (HMAC) along with its parallel implementation over several processors. Modal clustering techniques are especially designed to efficiently extract clusters in high dimensions with arbitrary density shapes. Further, clustering is performed over several resolutions and the results are summarized as a hierarchical tree, thus providing a model based multi resolution cluster analysis. Finally we implement a novel parallel implementation of HMAC which performs the clustering job over several processors thereby dramatically increasing the speed of clustering procedure especially for large data sets. This package also provides a number of functions for visualizing clusters in high dimensions, which can also be used with other clustering softwares.展开更多
文摘众数作为密度函数的最大值点,能有效刻画数据的集中趋势且对异常值具有较强稳健性。然而,在实际应用中,观测数据常因个体失访、退出实验或研究终止等原因出现右删失现象,且数据之间往往具有相依关系。为此,针对宽相依(widely orthant dependent,WOD)这一包含独立、负相依及部分正相依结构的宽泛相依序列,在右删失机制下结合逆概率加权(inverse probability weighting,IPW)方法构造核密度估计量,并据此提出众数的非参数核估计。在紧集和Lipschitz连续等适当条件下,证明密度估计量的一致强相合性,并进一步得出众数估计量的强相合性及其收敛速度。数值模拟和实证分析结果表明,该估计方法在有限样本下表现出良好的估计性能和稳健性,验证其渐近理论性质与实际应用价值。
基金Ministry of Science and Technology under Grant No.MOST 103-2815-C-019-003-E to the undergraduate studentthe NSC under Grant No.100-2221-E-019-040-MY3
文摘In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of Circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.
基金Argentinean National Council for Scientific Research (CONICET)the National University of San Juan (UNSJ) of ArgentinaNVIDIA Corporation for their support
文摘This article proposes a simultaneous localization and mapping(SLAM) version with continuous probabilistic mapping(CPSLAM), i.e., an algorithm of simultaneous localization and mapping that avoids the use of grids, and thus, does not require a discretized environment. A Markov random field(MRF) is considered to model this SLAM version with high spatial resolution maps. The mapping methodology is based on a point cloud generated by successive observations of the environment, which is kept bounded and representative by including a novel recursive subsampling method. The CP-SLAM problem is solved via iterated conditional modes(ICM), which is a classic algorithm with theoretical convergence over any MRF. The probabilistic maps are the most appropriate to represent dynamic environments, and can be easily implemented in other versions of the SLAM problem, such as the multi-robot version. Simulations and real experiments show the flexibility and excellent performance of this proposal.
文摘The number of modes (also known as modality) of a kernel density estimator (KDE) draws lots of interests and is important in practice. In this paper, we develop an inference framework on the modality of a KDE under multivariate setting using Gaussian kernel. We applied the modal clustering method proposed by [1] for mode hunting. A test statistic and its asymptotic distribution are derived to assess the significance of each mode. The inference procedure is applied on both simulated and real data sets.
文摘Modalclust is an R package which performs Hierarchical Mode Association Clustering (HMAC) along with its parallel implementation over several processors. Modal clustering techniques are especially designed to efficiently extract clusters in high dimensions with arbitrary density shapes. Further, clustering is performed over several resolutions and the results are summarized as a hierarchical tree, thus providing a model based multi resolution cluster analysis. Finally we implement a novel parallel implementation of HMAC which performs the clustering job over several processors thereby dramatically increasing the speed of clustering procedure especially for large data sets. This package also provides a number of functions for visualizing clusters in high dimensions, which can also be used with other clustering softwares.
