Due to coexistence of huge number of structural isomers,global search for the ground-state structures of atomic clusters is a challenging issue.The difficulty also originates from the computational cost of ab initio m...Due to coexistence of huge number of structural isomers,global search for the ground-state structures of atomic clusters is a challenging issue.The difficulty also originates from the computational cost of ab initio methods for describing the potential energy surface.Recently,machine learning techniques have been widely utilized to accelerate materials discovery and molecular simulation.Compared to the commonly used artificial neural network,graph network is naturally suitable for clusters with flexible geometric environment of each atom.Herein we develop a cluster graph attention network(CGANet)by aggregating information of neighboring vertices and edges using attention mechanism,which can precisely predict the binding energy and force of silver clusters with root mean square error of 5.4 meV/atom and mean absolute error of 42.3 meV/Å,respectively.As a proof-of-concept,we have performed global optimization of mediumsized Agn clusters(n=14–26)by combining CGANet and genetic algorithm.The reported ground-state structures for n=14–21,have been successfully reproduced,while entirely new lowest-energy structures are obtained for n=22–26.In addition to the description of potential energy surface,the CGANet is also applied to predict the electronic properties of clusters,such as HOMO energy and HOMO-LUMO gap.With accuracy comparable to ab initio methods and acceleration by at least two orders of magnitude,CGANet holds great promise in global search of lowest-energy structures of large clusters and inverse design of functional clusters.展开更多
We investigate the spectral approaches to the problem of point pattern matching, and present a spectral feature descriptors based on partial least square （PLS）. Given keypoints of two images, we define the position ...We investigate the spectral approaches to the problem of point pattern matching, and present a spectral feature descriptors based on partial least square （PLS）. Given keypoints of two images, we define the position similarity matrices respectively, and extract the spectral features from the matrices by PLS, which indicate geometric distribution and inner relationships of the keypoints. Then the keypoints matching is done by bipartite graph matching. The experiments on both synthetic and real-world data corroborate the robustness and invariance of the algorithm.展开更多
In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more tha...In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ（G） of the character degree graph △（G） of a solvable group G is a disjoint union ρ（G） =π1∪π2, where ｜πi｜≥2 and pi,qi∈πi for i = 1,2, and no vertex in πl is adjacent in △（G） to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.展开更多
In the deregulated economy, the maximum load forecasting is important for the electric industry. Many applications are included such as the energy generation and purchasing. The aim of the present study is to find the...In the deregulated economy, the maximum load forecasting is important for the electric industry. Many applications are included such as the energy generation and purchasing. The aim of the present study is to find the most suitable models for the peak load of the Kingdom of Bahrain. Many mathematical methods have been developing for maximum load forecasting. In the present paper, the modeling of the maximum load, population and GDP （gross domestic product） versus years obtained. The curve fitting technique used to find that models, where Graph 4.4.2 as a tool used to find the models. As well, Neuro-Fuzzy used to find the three models. Therefore, three techniques are used. These three are exponential, linear modeling and Neuro-Fuzzy. It is found that, the Neuro-Fuzzy is the most suitable and realistic one. Then, the linear modeling is the next suitable one.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11804076 and 91961204)the Fundamental Research Funds for the Central Universities of China(No.B210202151)the Changzhou Science and Technology Plan(No.CZ520012712).
文摘Due to coexistence of huge number of structural isomers,global search for the ground-state structures of atomic clusters is a challenging issue.The difficulty also originates from the computational cost of ab initio methods for describing the potential energy surface.Recently,machine learning techniques have been widely utilized to accelerate materials discovery and molecular simulation.Compared to the commonly used artificial neural network,graph network is naturally suitable for clusters with flexible geometric environment of each atom.Herein we develop a cluster graph attention network(CGANet)by aggregating information of neighboring vertices and edges using attention mechanism,which can precisely predict the binding energy and force of silver clusters with root mean square error of 5.4 meV/atom and mean absolute error of 42.3 meV/Å,respectively.As a proof-of-concept,we have performed global optimization of mediumsized Agn clusters(n=14–26)by combining CGANet and genetic algorithm.The reported ground-state structures for n=14–21,have been successfully reproduced,while entirely new lowest-energy structures are obtained for n=22–26.In addition to the description of potential energy surface,the CGANet is also applied to predict the electronic properties of clusters,such as HOMO energy and HOMO-LUMO gap.With accuracy comparable to ab initio methods and acceleration by at least two orders of magnitude,CGANet holds great promise in global search of lowest-energy structures of large clusters and inverse design of functional clusters.
基金supported by the Northwestern Polytechnical University Doctoral Dissertation Innovation Foundation (No. CX200819)the National Natural Science Foundation of China (No. 60375003)+1 种基金the Astronautics Basal Science Foundation of China (No. 03I53059)the Science and Technology Innovation Foundation of the Northwestern Polytechnical University(No. 2007KJ01033)
文摘We investigate the spectral approaches to the problem of point pattern matching, and present a spectral feature descriptors based on partial least square （PLS）. Given keypoints of two images, we define the position similarity matrices respectively, and extract the spectral features from the matrices by PLS, which indicate geometric distribution and inner relationships of the keypoints. Then the keypoints matching is done by bipartite graph matching. The experiments on both synthetic and real-world data corroborate the robustness and invariance of the algorithm.
文摘In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ（G） of the character degree graph △（G） of a solvable group G is a disjoint union ρ（G） =π1∪π2, where ｜πi｜≥2 and pi,qi∈πi for i = 1,2, and no vertex in πl is adjacent in △（G） to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.
文摘In the deregulated economy, the maximum load forecasting is important for the electric industry. Many applications are included such as the energy generation and purchasing. The aim of the present study is to find the most suitable models for the peak load of the Kingdom of Bahrain. Many mathematical methods have been developing for maximum load forecasting. In the present paper, the modeling of the maximum load, population and GDP （gross domestic product） versus years obtained. The curve fitting technique used to find that models, where Graph 4.4.2 as a tool used to find the models. As well, Neuro-Fuzzy used to find the three models. Therefore, three techniques are used. These three are exponential, linear modeling and Neuro-Fuzzy. It is found that, the Neuro-Fuzzy is the most suitable and realistic one. Then, the linear modeling is the next suitable one.
