We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis ...We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.展开更多
Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, especially for iterated set operations. A novel...Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, especially for iterated set operations. A novel and unified technique is proposed in this paper for computing single and iterated set operations efficiently, robustly and exactly. An adaptive octree is combined with a nested constructive solid geometry （CSG） tree by this technique. The intersection handling is restricted to the cells in the octree where intersection actually occurs. Within those cells, a CSG tree template is instanced by the surfaces and the tree is converted to planebased binary space partitioning （BSP） for set evaluation; Moreover, the surface classification is restricted to the ceils in the octree where the surfaces only come from a model and are within the bounding-boxes of other polyhedrons. These two ways bring about the efficiency and scalability of the operations, in terms of runtime and memory. As all surfaces in such a cell have the same classification relation, they are classified as a whole. Robustness and exactness are achieved by integrating plane-based geometry representation with adaptive geometry predicate technique in intersection handling, and by applying divide-and-conquer arithmetic on surface classification. Experimental results demonstrate that the proposed approach can guarantee the robustness of Boolean computations and runs faster than other existing approaches.展开更多
At nomaly detectors are used to distinguish differences between normal and abnormal data,which are usually implemented by evaluating and ranking the anomaly scores of each instance.A static unsupervised streaming anom...At nomaly detectors are used to distinguish differences between normal and abnormal data,which are usually implemented by evaluating and ranking the anomaly scores of each instance.A static unsupervised streaming anomaly detector is difficult to dynamically adjust anomaly score calculation.In real scenarios,anomaly detection often needs to be regulated by human feedback,which benefits adjusting anomaly detectors.In this paper,we propose a human-machine interactive streaming anomaly detection method,named ISPForest,which can be adaptively updated online under the guidance of human feedback.In particular,the feedback will be used to adjust the anomaly score calculation and structure of the detector,ideally attaining more accurate anomaly scores in the future.Our main contribution is to improve the tree-based streaming anomaly detection model that can be updated online from perspectives of anomaly score calculation and model structure.Our approach is instantiated for the powerful class of tree-based streaming anomaly detectors,and we conduct experiments on a range of benchmark datasets.The results demonstrate that the utility of incorporating feedback can improve the performance of anomaly detectors with a few human efforts.展开更多
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the ...We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.展开更多
基金"This work is supported by the financial grant of DST/MS/150 2K".
文摘We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.
基金supported by the Natural Science Foundation of China under Grant No.61202154 and No.61133009the National Basic Research Project of China under Grant No.2011CB302203+2 种基金Shanghai Pujiang Program under Grant No.13PJ1404500the Science and Technology Commission of Shanghai Municipality Program under Grant No.13511505000the Open Project Program of the State Key Lab of CAD&CG of Zhejiang University under Grant No.A1401
文摘Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, especially for iterated set operations. A novel and unified technique is proposed in this paper for computing single and iterated set operations efficiently, robustly and exactly. An adaptive octree is combined with a nested constructive solid geometry （CSG） tree by this technique. The intersection handling is restricted to the cells in the octree where intersection actually occurs. Within those cells, a CSG tree template is instanced by the surfaces and the tree is converted to planebased binary space partitioning （BSP） for set evaluation; Moreover, the surface classification is restricted to the ceils in the octree where the surfaces only come from a model and are within the bounding-boxes of other polyhedrons. These two ways bring about the efficiency and scalability of the operations, in terms of runtime and memory. As all surfaces in such a cell have the same classification relation, they are classified as a whole. Robustness and exactness are achieved by integrating plane-based geometry representation with adaptive geometry predicate technique in intersection handling, and by applying divide-and-conquer arithmetic on surface classification. Experimental results demonstrate that the proposed approach can guarantee the robustness of Boolean computations and runs faster than other existing approaches.
基金supported in part by the National Science Fund for Distinguished Young Scholars(61725205)the National Natural Science Foundation of China(Grant Nos.61960206008,61772428,61972319,and61902320).
文摘At nomaly detectors are used to distinguish differences between normal and abnormal data,which are usually implemented by evaluating and ranking the anomaly scores of each instance.A static unsupervised streaming anomaly detector is difficult to dynamically adjust anomaly score calculation.In real scenarios,anomaly detection often needs to be regulated by human feedback,which benefits adjusting anomaly detectors.In this paper,we propose a human-machine interactive streaming anomaly detection method,named ISPForest,which can be adaptively updated online under the guidance of human feedback.In particular,the feedback will be used to adjust the anomaly score calculation and structure of the detector,ideally attaining more accurate anomaly scores in the future.Our main contribution is to improve the tree-based streaming anomaly detection model that can be updated online from perspectives of anomaly score calculation and model structure.Our approach is instantiated for the powerful class of tree-based streaming anomaly detectors,and we conduct experiments on a range of benchmark datasets.The results demonstrate that the utility of incorporating feedback can improve the performance of anomaly detectors with a few human efforts.
文摘We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.
