Optimized Query Algorithms for Top- K Group Skyline

Skyline query is a typical multiobjective query and optimization problem, which aims to find out the information that all users may be interested in a multidimensional data set. Multiobjective optimization has been applied in many scientific fields, including engineering, economy, and logistics. It is necessary to make the optimal decision when two or more conflicting objectives are weighed. For example, maximize the service area without changing the number of express points, and in the existing business district distribution, find out the area or target point set whose target attribute is most in line with the user’s interest. Group Skyline is a further extension of the traditional definition of Skyline. It considers not only a single point but a group of points composed of multiple points. These point groups should not be dominated by other point groups. For example, in the previous example of business district selection, a single target point in line with the user’s interest is not the focus of the research, but the overall optimality of all points in the whole target area is the final result that the user wants. This paper focuses on how to efficiently solve top- k group Skyline query problem. Firstly, based on the characteristics that the low levels of Skyline dominate the high level points, a group Skyline ranking strategy and the corresponding SLGS algorithm on Skyline layer are proposed according to the number of Skyline layer and vertices in the layer. Secondly, a group Skyline ranking strategy based on vertex coverage is proposed, and corresponding VCGS algorithm and optimized algorithm VCGS+ are proposed. Finally, experiments verify the effectiveness of this method from two aspects: query response time and the quality of returned results.

The determination of point groups from imprecise molecular geometries

We present a new approach for the assignment of a point group to a molecule when the structure conforms only approximately to the symmetry. It proceeds by choosing a coordinate frame that minimises a measure of symmetry breaking that is computed efficiently as a simple function of the molecular coordinates and point group specification.

MPCR-Net: Multiple Partial Point Clouds Registration Network Using a Global Template

With advancements in photoelectric technology and computer image processing technology, the visual measurement method based on point clouds is gradually being applied to the 3D measurement of large workpieces. Point cloud registration is a key step in 3D measurement, and its registration accuracy directly affects the accuracy of 3D measurements. In this study, we designed a novel MPCR-Net for multiple partial point cloud registration networks. First, an ideal point cloud was extracted from the CAD model of the workpiece and used as the global template. Next, a deep neural network was used to search for the corresponding point groups between each partial point cloud and the global template point cloud. Then, the rigid body transformation matrix was learned according to these correspondence point groups to realize the registration of each partial point cloud. Finally, the iterative closest point algorithm was used to optimize the registration results to obtain the final point cloud model of the workpiece. We conducted point cloud registration experiments on untrained models and actual workpieces, and by comparing them with existing point cloud registration methods, we verified that the MPCR-Net could improve the accuracy and robustness of the 3D point cloud registration.

Multi-class, multi-functional design of photonic topological insulators by rational symmetry-indicators engineering

An explicit topology optimization-based design paradigm is proposed for the design of photonic topological crystalline insulators (TCIs). To strictly guarantee the topological property, rational engineering of symmetry-indicators is carried out by mathematical programming, which simultaneously maximizes the width of nontrivial topological band gaps and achieves the desired quantized bulk polarization. Our approach is successfully applied to design photonic TCIs with time-reversal symmetry in two-dimensional point groups, higher-order magnetic TCIs, and higher-order photonic TCIs. This methodology paves the way for inverse design of optimized photonic/phononic, multiphysics, and multifunctional three-dimensional TCIs.

SINIF CEBİRİ YAKLAŞIMI ALTINDA 𝑫𝟐𝒅 ve 𝑪𝟑𝒊 NOKTA GRUPLARI

In this study, the point groups 𝐷2𝑑 and 𝐶3𝑖 which belong to tetragonal and trigonal crystal systems, respectively, are handled under the class sum approach. Symmetry groups were formed with symmetry elements that left these point groups unchanged and Cayley tables of related groups were obtained. Using these tables, the conjugates of the elements and the classes of the group were formed. Secular equations are written for each class sum obtained by the sum of the elements that make up the class. By solving these secular equations, the character vectors are obtained. Thus, the character tables were reconstructed with the calculated characters for both point groups under the class sum approach.

MPCR-Net: Multiple Partial Point Clouds Registration Network Using a Global Template

With the advancement of photoelectric technology and computer image processing technology, the visual measurement method based on point clouds is gradually applied to the 3D measurement of large workpieces. Point cloud registration is a key step in 3D measurement, and its registration accuracy directly affects the accuracy of 3D measurements. In this study, we designed a novel MPCR-Net for multiple partial point cloud registration networks. First, an ideal point cloud was extracted from the CAD model of the workpiece and was used as the global template. Next, a deep neural network was used to search for the corresponding point groups between each partial point cloud and the global template point cloud. Then, the rigid body transformation matrix was learned according to these correspondence point groups to realize the registration of each partial point cloud. Finally, the iterative closest point algorithm was used to optimize the registration results to obtain a final point cloud model of the workpiece. We conducted point cloud registration experiments on untrained models and actual workpieces, and by comparing them with existing point cloud registration methods, we verified that the MPCR-Net could improve the accuracy and robustness of the 3D point cloud registration.