We propose a new framework for the sampling,compression,and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces.Our approach involves constructing a tensor called the RaySe...We propose a new framework for the sampling,compression,and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces.Our approach involves constructing a tensor called the RaySense sketch,which captures nearest neighbors from the underlying geometry of points along a set of rays.We explore various operations that can be performed on the RaySense sketch,leading to different properties and potential applications.Statistical information about the data set can be extracted from the sketch,independent of the ray set.Line integrals on point sets can be efficiently computed using the sketch.We also present several examples illustrating applications of the proposed strategy in practical scenarios.展开更多
In this paper,a Voronoi cell finite element model is developed to study the microscopic and macroscopic mechanical behaviors of heterogenous materials,including arbitrary distributed heterogeneity(inclusions or fibers...In this paper,a Voronoi cell finite element model is developed to study the microscopic and macroscopic mechanical behaviors of heterogenous materials,including arbitrary distributed heterogeneity(inclusions or fibers)coated with interphase layers,based on linear elasticity theory.The interphase between heterogeneity and a matrix are regarded as in the third phase(elastic layers),in contrast to the perfect interface of the spring-like Voronoi cell finite element model(VCFEM)in the literature.In this model,both stress and the displacement field are assumed to be independent in an element.Formulations of stress are derived for each of the three phases in an element,as is the type of functional.Numerical examples were used to study the microscopic and macroscopic properties,such as the effective modulus,of the composites.The results of the proposed VCFEM were compared with analytical solution and numerical results obtained from a standard finite element analysis to confirm its effectiveness.展开更多
Ambient noise tomography,when applied to a dense linear seismic array,has the capability to provide detailed insights into the fine velocity structures across diverse tectonic settings.The linear station arrangement n...Ambient noise tomography,when applied to a dense linear seismic array,has the capability to provide detailed insights into the fine velocity structures across diverse tectonic settings.The linear station arrangement naturally generates parallel and concentrated ray paths along the array trend.This unique geometry requires specific optimization of the inversion methodology and model parameterization.The Bayesian-based transdimensional inversion method,characterized by its fully non-linear nature and high degree of freedom in parameter settings,offers a powerful tool for ambient noise inversion.To effectively adapt this method to a linear array layout,we propose a modification to the Voronoi cell tessellation built in the transdimensional method.By introducing spatial priority to the Voronoi kernels,we strategically increased the density of Voronoi cells along the direction of the array.We then applied the modified approach to a linear seismic array in the North China Craton and validated its robustness through phase velocity images and resolution tests.Our improved non-uniform sampling technique in the 2-D model space accelerates convergence while simultaneously enhancing model accuracy.Compared with the conventional damped leastsquares method,the proposed algorithm revealed a shear-wave velocity map with notable low-velocity anomalies situated in the middle and lower crust beneath the borders of the Ordos block and its surrounding orogenic belt.Aligned with the crustal structures revealed by receiver function and electrical imaging,our findings indicated that the western and eastern margins of the Ordos block had experienced intensive crustal wedge deformation and re-melting,respectively.展开更多
Reverse k nearest neighbor （RNNk） is a generalization of the reverse nearest neighbor problem and receives increasing attention recently in the spatial data index and query. RNNk query is to retrieve all the data po...Reverse k nearest neighbor （RNNk） is a generalization of the reverse nearest neighbor problem and receives increasing attention recently in the spatial data index and query. RNNk query is to retrieve all the data points which use a query point as one of their k nearest neighbors. To answer the RNNk of queries efficiently, the properties of the Voronoi cell and the space-dividing regions are applied. The RNNk of the given point can be found without computing its nearest neighbors every time by using the rank Voronoi cell. With the elementary RNNk query result, the candidate data points of reverse nearest neighbors can he further limited by the approximation with sweepline and the partial extension of query region Q. The approximate minimum average distance （AMAD） can be calculated by the approximate RNNk without the restriction of k. Experimental results indicate the efficiency and the effectiveness of the algorithm and the approximate method in three varied data distribution spaces. The approximate query and the calculation method with the high precision and the accurate recall are obtained by filtrating data and pruning the search space.展开更多
基金supported by the National Science Foundation(Grant No.DMS-1440415)partially supported by a grant from the Simons Foundation,NSF Grants DMS-1720171 and DMS-2110895a Discovery Grant from Natural Sciences and Engineering Research Council of Canada.
文摘We propose a new framework for the sampling,compression,and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces.Our approach involves constructing a tensor called the RaySense sketch,which captures nearest neighbors from the underlying geometry of points along a set of rays.We explore various operations that can be performed on the RaySense sketch,leading to different properties and potential applications.Statistical information about the data set can be extracted from the sketch,independent of the ray set.Line integrals on point sets can be efficiently computed using the sketch.We also present several examples illustrating applications of the proposed strategy in practical scenarios.
基金supported by the National Natural Science Foundation of China(Grants 11402103 and 11572142).
文摘In this paper,a Voronoi cell finite element model is developed to study the microscopic and macroscopic mechanical behaviors of heterogenous materials,including arbitrary distributed heterogeneity(inclusions or fibers)coated with interphase layers,based on linear elasticity theory.The interphase between heterogeneity and a matrix are regarded as in the third phase(elastic layers),in contrast to the perfect interface of the spring-like Voronoi cell finite element model(VCFEM)in the literature.In this model,both stress and the displacement field are assumed to be independent in an element.Formulations of stress are derived for each of the three phases in an element,as is the type of functional.Numerical examples were used to study the microscopic and macroscopic properties,such as the effective modulus,of the composites.The results of the proposed VCFEM were compared with analytical solution and numerical results obtained from a standard finite element analysis to confirm its effectiveness.
基金funded by the Special Fund of the Institute of Geophysics,China Earthquake Administration (Nos.DQJB21K52,and DQJB22R33)。
文摘Ambient noise tomography,when applied to a dense linear seismic array,has the capability to provide detailed insights into the fine velocity structures across diverse tectonic settings.The linear station arrangement naturally generates parallel and concentrated ray paths along the array trend.This unique geometry requires specific optimization of the inversion methodology and model parameterization.The Bayesian-based transdimensional inversion method,characterized by its fully non-linear nature and high degree of freedom in parameter settings,offers a powerful tool for ambient noise inversion.To effectively adapt this method to a linear array layout,we propose a modification to the Voronoi cell tessellation built in the transdimensional method.By introducing spatial priority to the Voronoi kernels,we strategically increased the density of Voronoi cells along the direction of the array.We then applied the modified approach to a linear seismic array in the North China Craton and validated its robustness through phase velocity images and resolution tests.Our improved non-uniform sampling technique in the 2-D model space accelerates convergence while simultaneously enhancing model accuracy.Compared with the conventional damped leastsquares method,the proposed algorithm revealed a shear-wave velocity map with notable low-velocity anomalies situated in the middle and lower crust beneath the borders of the Ordos block and its surrounding orogenic belt.Aligned with the crustal structures revealed by receiver function and electrical imaging,our findings indicated that the western and eastern margins of the Ordos block had experienced intensive crustal wedge deformation and re-melting,respectively.
基金Supported by the National Natural Science Foundation of China (60673136)the Natural Science Foundation of Heilongjiang Province of China (F200601)~~
文摘Reverse k nearest neighbor （RNNk） is a generalization of the reverse nearest neighbor problem and receives increasing attention recently in the spatial data index and query. RNNk query is to retrieve all the data points which use a query point as one of their k nearest neighbors. To answer the RNNk of queries efficiently, the properties of the Voronoi cell and the space-dividing regions are applied. The RNNk of the given point can be found without computing its nearest neighbors every time by using the rank Voronoi cell. With the elementary RNNk query result, the candidate data points of reverse nearest neighbors can he further limited by the approximation with sweepline and the partial extension of query region Q. The approximate minimum average distance （AMAD） can be calculated by the approximate RNNk without the restriction of k. Experimental results indicate the efficiency and the effectiveness of the algorithm and the approximate method in three varied data distribution spaces. The approximate query and the calculation method with the high precision and the accurate recall are obtained by filtrating data and pruning the search space.
