A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism a...A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s＋1 links from an s-link mechanism （the final configuration）. The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.展开更多
The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can ea...The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of metamorphic mechanisms because it can only be used in the topological representation of mechanisms with single joints.In order to overcome the drawback of the adjacency matrix,a kind of new matrix named as extended adjacency matrix is proposed to express topological structures of all mechanisms.The extended adjacency matrix is not only suitable for the topological representation of mechanisms with single joints,but also can be used in that of mechanisms with multiple joints.On this basis,a method of matrix operations based on the extended adjacency matrix is proposed to analyze the configuration transformation of metamorphic mechanisms.The method is not only suitable for configuration analysis of metamorphic mechanisms with single joints as well as metamorphic mechanisms with multiple joints.The method is evaluated by calculating two examples representing metamorphic mechanisms with single joint and multiple joints respectively.It can be concluded that the method is effective and correct for analysis of configuration transformation of all metamorphic mechanisms.The proposed method is simple and easy to be achieved by computer programming.It provides a basis for structural synthesis of all metamorphic mechanisms.展开更多
This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, ...This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.展开更多
The relation is a semantic expression relevant to two named entities in a sentence.Since a sentence usually contains several named entities,it is essential to learn a structured sentence representation that encodes de...The relation is a semantic expression relevant to two named entities in a sentence.Since a sentence usually contains several named entities,it is essential to learn a structured sentence representation that encodes dependency information specific to the two named entities.In related work,graph convolutional neural networks are widely adopted to learn semantic dependencies,where a dependency tree initializes the adjacency matrix.However,this approach has two main issues.First,parsing a sentence heavily relies on external toolkits,which can be errorprone.Second,the dependency tree only encodes the syntactical structure of a sentence,which may not align with the relational semantic expression.In this paper,we propose an automatic graph learningmethod to autonomously learn a sentence’s structural information.Instead of using a fixed adjacency matrix initialized by a dependency tree,we introduce an Adaptive Adjacency Matrix to encode the semantic dependency between tokens.The elements of thismatrix are dynamically learned during the training process and optimized by task-relevant learning objectives,enabling the construction of task-relevant semantic dependencies within a sentence.Our model demonstrates superior performance on the TACRED and SemEval 2010 datasets,surpassing previous works by 1.3%and 0.8%,respectively.These experimental results show that our model excels in the relation extraction task,outperforming prior models.展开更多
The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries an...The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.展开更多
The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t...The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t, the problem of determining the value of ex(m,n;Km−t,n−t)has been solved by Balbuena et al. in 2007, whose proof focuses on the structural analysis of bipartite graphs. In this paper, we provide a new proof on the value of ex(m,n;Km−t,n−t)by virtue of algebra method with the tool of adjacency matrices of bipartite graphs, which is inspired by the method using { 0,1 }-matrices due to Zarankiewicz [Problem P 101. Colloquium Mathematicum, 2(1951), 301].展开更多
Data exploration,usually the first step in data analysis,is a useful method to tackle challenges caused by big geoscience data.It conducts quick analysis of data,investigates the patterns,and generates/refines researc...Data exploration,usually the first step in data analysis,is a useful method to tackle challenges caused by big geoscience data.It conducts quick analysis of data,investigates the patterns,and generates/refines research questions to guide advanced statistics and machine learning algorithms.The background of this work is the open mineral data provided by several sources,and the focus is different types of associations in mineral properties and occurrences.Researchers in mineralogy have been applying different techniques for exploring such associations.Although the explored associations can lead to new scientific insights that contribute to crystallography,mineralogy,and geochemistry,the exploration process is often daunting due to the wide range and complexity of factors involved.In this study,our purpose is implementing a visualization tool based on the adjacency matrix for a variety of datasets and testing its utility for quick exploration of association patterns in mineral data.Algorithms,software packages,and use cases have been developed to process a variety of mineral data.The results demonstrate the efficiency of adjacency matrix in real-world usage.All the developed works of this study are open source and open access.展开更多
The occurrence of local circulating ventilation can be caused by many factors, such as the airflow reversion during mine fire,the improper arrangement of local fan or underground fan station and the man-made error inp...The occurrence of local circulating ventilation can be caused by many factors, such as the airflow reversion during mine fire,the improper arrangement of local fan or underground fan station and the man-made error input of raw data before network solving. Once circulating ventilations occur,the corresponding branches in the ventilation network corresponding to the relevant airways in ventilation system form circuits,and all the direc- tions of the branches in the circuits are identical,which is the unidirectional problem in ventilation network.Based on the properties of node adjacent matrix,a serial of mathe- matical computation to node adjacent matrix were performed,and a mathematical model for determining unidirectional circuits based on node adjacent matrix was put forward.展开更多
In order to discover the probability distribution feature of edge in aviation network adjacent matrix of China and on the basis of this feature to establish an algorithm of searching non-overlap community structure in...In order to discover the probability distribution feature of edge in aviation network adjacent matrix of China and on the basis of this feature to establish an algorithm of searching non-overlap community structure in network to reveal the inner principle of complex network with the feature of small world in aspect of adjacent matrix and community structure,aviation network adjacent matrix of China was transformed according to the node rank and the matrix was arranged on the basis of ascending node rank with the center point as original point.Adjacent probability from the original point to extension around in approximate area was calculated.Through fitting probability distribution curve,power function of probability distribution of edge in adjacent matrix arranged by ascending node rank was found.According to the feature of adjacent probability distribution,deleting step by step with node rank ascending algorithm was set up to search non-overlap community structure in network and the flow chart of algorithm was given.A non-overlap community structure with 10 different scale communities in aviation network of China was found by the computer program written on the basis of this algorithm.展开更多
Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-grap...Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-graph,represented byθ(a1,a2,a3).The graph obtained by bonding the two end vertices of the path Ps to the vertices of theθ(a1,a2,a3)andθ(b1,b2,b3)of degree three,respectively,is denoted byα(a1,a2,a3,s,b1,b2,b3)and calledα-graph.β-graph is denoted whenβ(a1,a2,a3,b1,b2,b3)=α(a1,a2,a3,1,b1,b2,b3).In this paper,we give the necessary and sufficient conditions for the singularity ofα-graph andβ-graph,and prove that the probability that a random givenα-graph andβ-graph is a singular graph is equal to 14232048 and 733/1024,respectively.展开更多
In today's world, various approaches and parameters exist for designing a plan and determining its spatial, placement. Hence, various modes for identifying crucial locations can be explored when an architectural p...In today's world, various approaches and parameters exist for designing a plan and determining its spatial, placement. Hence, various modes for identifying crucial locations can be explored when an architectural plan is designed in different dimensions. While designing all these modes takes considerable time, there are numerous potential applications for artificial intelligence (AI) in this domain. This study aims to compute and use an adjacency matrix to generate architectural residential plans. Additionally, it develops a plan generation algorithm in Rhinoceros software, utilizing the Grasshopper plugin to create a dataset of architectural plans. In the following step, the data was entered into a neural network to identify the architectural plan's type, furniture, icons, and use of spaces, which was achieved using YOLOv4, EfficientDet, YOLOv5, DetectoRS, and RetinaNet. The algorithm's execution, testing, and training were conducted using Darknet and PyTorch. The research dataset comprises 12,000 plans, with 70% employed in the training phase and 30% in the testing phase. The network was appropriately trained practically and precisely in relation to an average precision (AP) resulting of 91.50%. After detecting the types of space use, the main research algorithm has been designed and coded, which includes determining the adjacency matrix of architectural plan spaces in seven stages. All research processes were conducted in Python, including dataset preparation, network object detection, and adjacency matrix algorithm design. Finally, the adjacency matrix is given to the input of the proposed plan generator network, which consequently, based on the resulting adjacency, obtains different placement modes for spaces and furniture.展开更多
In this article, we introduce the Google＇s method for quality ranking of web page in a formal mathematical format, use the power iteration to improve the PageRank, and also discuss the effect of different q to the Pa...In this article, we introduce the Google＇s method for quality ranking of web page in a formal mathematical format, use the power iteration to improve the PageRank, and also discuss the effect of different q to the PageRank, as well as how a PageRank will be changed if more links are added to one page or removed from some pages.展开更多
The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector <em>e<sub>j</sub></em> =(0, <span style="font-size:12.8px;white-space:normal;&...The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector <em>e<sub>j</sub></em> =(0, <span style="font-size:12.8px;white-space:normal;">…</span> , 1, … , 0)<sup>T</sup> and the all -1 vector <em>j</em> =(1, 1, <span style="font-size:12.8px;white-space:normal;">…</span>,1)<sup>T</sup>, the cosine of the (acute) angle formed by the vector <em>e<sub>j</sub></em> and the eigensubspace is called an angle of the graph. The cosine of the (acute) angle formed by the vector <em>j</em> and the eigensubspace is called a main angle of the graph. The angles and main angles are all important parameters on the graph, and they can be combined with the eigenvalues of the graph to determine the degree sequence of the graph, the number of triangles, quadrilaterals and pentagons on the graph, and the characteristic polynomials of the complement graph, but there is little study on the angles and main angles of the graph. In this paper, we determine the angles and main angles of the complete graph, the cube graph, the Petersen graph, the cycle and the complete bipartite graph.展开更多
Fischer-Tropsch synthesis(FTS)wax is a mixture of linear hydrocarbons with carbon number from C7 to C70+.Converting FTS wax into high-quality diesel(no sulfur and nitrogen contents)by hydrocracking technology is attra...Fischer-Tropsch synthesis(FTS)wax is a mixture of linear hydrocarbons with carbon number from C7 to C70+.Converting FTS wax into high-quality diesel(no sulfur and nitrogen contents)by hydrocracking technology is attractive in economy and practicability.Kinetic study of the hydrocracking of FTS wax in elementary step level is very challenging because of the huge amounts of reactions and species involved.Generation of reaction networks for hydrocracking of FTS wax in which the chain length goes up to C70 is described on the basis of Boolean adjacency matrixes.Each of the species(including paraffins,olefins and carbenium ions)involved in the elementary steps is represented digitally by using a(N+3)N matrix,in which a group of standardized numbering rules are designed to guarantee the unique identity of the species.Subsequently,the elementary steps are expressed by computer-aided matrix transformations in terms of proposed reaction rules.Dynamic memory allocation is used in species storage and a characteristic vector with nine elements is designed to store the key information of a(N+3)N matrix,which obviously reduces computer memory consumption and improves computing efficiency.The detailed reaction networks of FTS wax hydrocracking can be generated smoothly and accurately by the current method.The work is the basis of advanced elementary-step-level kinetic modeling.展开更多
In this paper,based on the adjacency matrix of the network and its powers,the formulas are derived for theshortest path and the average path length,and an effective algorithm is presented.Furthermore,an example is pro...In this paper,based on the adjacency matrix of the network and its powers,the formulas are derived for theshortest path and the average path length,and an effective algorithm is presented.Furthermore,an example is providedto demonstrate the proposed method.展开更多
The mechanism of three⁃order Rubiks Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as...The mechanism of three⁃order Rubiks Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as the research object,and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC.In this paper,the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom,establishing a set of adjacency matrix,and determining the degree of freedom of the RC which is attributed to the number of non⁃zero elements in the set of adjacent matrix.The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC,which is simple and convenient for computer processing.The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science.Meanwhile,it is of great significance to the study of other complex mechanisms with variable degrees of freedom.展开更多
The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determi...The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.展开更多
Technically, a group of more than two wheeled mobile robots working collectively towards a common goal are known as a multi-robot system. An increasing number of industries have implemented multi-robot systems to elim...Technically, a group of more than two wheeled mobile robots working collectively towards a common goal are known as a multi-robot system. An increasing number of industries have implemented multi-robot systems to eliminate the risk of human injuries while working on hazardous tasks, and to improve productivity. Globally, engineers are continuously researching better, simple, and faster cooperative Control algorithms to provide a Control strategy where each agent in the robot formation can communicate effectively and achieve a consensus in their position, orientation and speed.<span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">This paper explores a novel Formation Building Algorithm and its global stability around a configuration vector. A simulation in MATLAB</span><sup><span style="font-size:12px;font-family:Verdana;"><span lang="ZH-CN" style="font-size:12pt;font-family:宋体;">?</span></span></sup><span style="font-family:Verdana;"> was carried out to examine the performance of the Algorithm for two geometric formations and a fixed number of robots. In addition, an obstacle avoidance technique was presented assuming that all robots are equipped with range sensors. In particular, a uniform rounded obstacle is used to analyze</span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">the performance of the technique with the use of detailed geometric calculations.</span>展开更多
In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the ad...In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.展开更多
The generating function for generating integer sequence of Aunu numbers of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator on the function for where the op...The generating function for generating integer sequence of Aunu numbers of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator on the function for where the operation induces addition or subtraction on the pairs of ai, aj elements which are consecutive pairs of elements obtained from a generating set of some finite order. The paper identifies that the set of the generated pairs of integer sequence is non-associative. The paper also presents the graph theoretic applications of the integers generated in which subgraphs are deduced from the main graph and adjacency matrices and incidence matrices constructed. It was also established that some of the subgraphs were found to be regular graphs. The findings in this paper can further be used in coding theory, Boolean algebra and circuit designs.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 51075039, Grant No. 50805110,Grant No. 50705010)Beijing Municipal Natural Science Foundation of China (Grant No. 3082014)the Fundamental Research Funds for the Central Universities of China (Grant No. 2009CZ08, Grant No. JY10000904010)
文摘A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s＋1 links from an s-link mechanism （the final configuration）. The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.
基金supported by National Natural Science Foundation of China (Grant No. 51075039, Grant No. 50705010)Beijing Municipal Natural Science Foundation of China (Grant No. 3082014, Grant No.3053017)Fundamental Research Funds for the Central Universities of China (Grant No. 2009CZ08)
文摘The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of metamorphic mechanisms because it can only be used in the topological representation of mechanisms with single joints.In order to overcome the drawback of the adjacency matrix,a kind of new matrix named as extended adjacency matrix is proposed to express topological structures of all mechanisms.The extended adjacency matrix is not only suitable for the topological representation of mechanisms with single joints,but also can be used in that of mechanisms with multiple joints.On this basis,a method of matrix operations based on the extended adjacency matrix is proposed to analyze the configuration transformation of metamorphic mechanisms.The method is not only suitable for configuration analysis of metamorphic mechanisms with single joints as well as metamorphic mechanisms with multiple joints.The method is evaluated by calculating two examples representing metamorphic mechanisms with single joint and multiple joints respectively.It can be concluded that the method is effective and correct for analysis of configuration transformation of all metamorphic mechanisms.The proposed method is simple and easy to be achieved by computer programming.It provides a basis for structural synthesis of all metamorphic mechanisms.
基金Project supported by Science Foundation of Shanghai MunicipalConmission of Education (Grant No .03A203)
文摘This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.
基金supported by the Technology Projects of Guizhou Province under Grant[2024]003National Natural Science Foundation of China(GrantNos.62166007,62066008,62066007)Guizhou Provincial Science and Technology Projects under Grant No.ZK[2023]300.
文摘The relation is a semantic expression relevant to two named entities in a sentence.Since a sentence usually contains several named entities,it is essential to learn a structured sentence representation that encodes dependency information specific to the two named entities.In related work,graph convolutional neural networks are widely adopted to learn semantic dependencies,where a dependency tree initializes the adjacency matrix.However,this approach has two main issues.First,parsing a sentence heavily relies on external toolkits,which can be errorprone.Second,the dependency tree only encodes the syntactical structure of a sentence,which may not align with the relational semantic expression.In this paper,we propose an automatic graph learningmethod to autonomously learn a sentence’s structural information.Instead of using a fixed adjacency matrix initialized by a dependency tree,we introduce an Adaptive Adjacency Matrix to encode the semantic dependency between tokens.The elements of thismatrix are dynamically learned during the training process and optimized by task-relevant learning objectives,enabling the construction of task-relevant semantic dependencies within a sentence.Our model demonstrates superior performance on the TACRED and SemEval 2010 datasets,surpassing previous works by 1.3%and 0.8%,respectively.These experimental results show that our model excels in the relation extraction task,outperforming prior models.
基金supported by the China Scholarship Council and the CERNET Innovation Project under grant No.20170111.
文摘The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.
文摘The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t, the problem of determining the value of ex(m,n;Km−t,n−t)has been solved by Balbuena et al. in 2007, whose proof focuses on the structural analysis of bipartite graphs. In this paper, we provide a new proof on the value of ex(m,n;Km−t,n−t)by virtue of algebra method with the tool of adjacency matrices of bipartite graphs, which is inspired by the method using { 0,1 }-matrices due to Zarankiewicz [Problem P 101. Colloquium Mathematicum, 2(1951), 301].
基金supported by the U.S.National Science Foundation(Grant No.2126315).
文摘Data exploration,usually the first step in data analysis,is a useful method to tackle challenges caused by big geoscience data.It conducts quick analysis of data,investigates the patterns,and generates/refines research questions to guide advanced statistics and machine learning algorithms.The background of this work is the open mineral data provided by several sources,and the focus is different types of associations in mineral properties and occurrences.Researchers in mineralogy have been applying different techniques for exploring such associations.Although the explored associations can lead to new scientific insights that contribute to crystallography,mineralogy,and geochemistry,the exploration process is often daunting due to the wide range and complexity of factors involved.In this study,our purpose is implementing a visualization tool based on the adjacency matrix for a variety of datasets and testing its utility for quick exploration of association patterns in mineral data.Algorithms,software packages,and use cases have been developed to process a variety of mineral data.The results demonstrate the efficiency of adjacency matrix in real-world usage.All the developed works of this study are open source and open access.
基金National Nature Science Foundation of China(50704019)Nature Science Foundation of Liaoning Province(20062204)
文摘The occurrence of local circulating ventilation can be caused by many factors, such as the airflow reversion during mine fire,the improper arrangement of local fan or underground fan station and the man-made error input of raw data before network solving. Once circulating ventilations occur,the corresponding branches in the ventilation network corresponding to the relevant airways in ventilation system form circuits,and all the direc- tions of the branches in the circuits are identical,which is the unidirectional problem in ventilation network.Based on the properties of node adjacent matrix,a serial of mathe- matical computation to node adjacent matrix were performed,and a mathematical model for determining unidirectional circuits based on node adjacent matrix was put forward.
基金National Natural Science Foundation of China(71971017).
文摘In order to discover the probability distribution feature of edge in aviation network adjacent matrix of China and on the basis of this feature to establish an algorithm of searching non-overlap community structure in network to reveal the inner principle of complex network with the feature of small world in aspect of adjacent matrix and community structure,aviation network adjacent matrix of China was transformed according to the node rank and the matrix was arranged on the basis of ascending node rank with the center point as original point.Adjacent probability from the original point to extension around in approximate area was calculated.Through fitting probability distribution curve,power function of probability distribution of edge in adjacent matrix arranged by ascending node rank was found.According to the feature of adjacent probability distribution,deleting step by step with node rank ascending algorithm was set up to search non-overlap community structure in network and the flow chart of algorithm was given.A non-overlap community structure with 10 different scale communities in aviation network of China was found by the computer program written on the basis of this algorithm.
基金Supported by National Natural Science Foundation of China(Grant No.11561056)National Natural Science Foundation of Qinghai Provence(Grant No.2022-ZJ-924)Innovation Project of Qinghai Minzu University(Grant No.07M2022002).
文摘Let G be a finite simple graph and A(G)be its adjacency matrix.Then G is singular if A(G)is singular.The graph obtained by bonding the starting ver-tices and ending vertices of three paths Pa1,Pa2,Pa3 is calledθ-graph,represented byθ(a1,a2,a3).The graph obtained by bonding the two end vertices of the path Ps to the vertices of theθ(a1,a2,a3)andθ(b1,b2,b3)of degree three,respectively,is denoted byα(a1,a2,a3,s,b1,b2,b3)and calledα-graph.β-graph is denoted whenβ(a1,a2,a3,b1,b2,b3)=α(a1,a2,a3,1,b1,b2,b3).In this paper,we give the necessary and sufficient conditions for the singularity ofα-graph andβ-graph,and prove that the probability that a random givenα-graph andβ-graph is a singular graph is equal to 14232048 and 733/1024,respectively.
文摘In today's world, various approaches and parameters exist for designing a plan and determining its spatial, placement. Hence, various modes for identifying crucial locations can be explored when an architectural plan is designed in different dimensions. While designing all these modes takes considerable time, there are numerous potential applications for artificial intelligence (AI) in this domain. This study aims to compute and use an adjacency matrix to generate architectural residential plans. Additionally, it develops a plan generation algorithm in Rhinoceros software, utilizing the Grasshopper plugin to create a dataset of architectural plans. In the following step, the data was entered into a neural network to identify the architectural plan's type, furniture, icons, and use of spaces, which was achieved using YOLOv4, EfficientDet, YOLOv5, DetectoRS, and RetinaNet. The algorithm's execution, testing, and training were conducted using Darknet and PyTorch. The research dataset comprises 12,000 plans, with 70% employed in the training phase and 30% in the testing phase. The network was appropriately trained practically and precisely in relation to an average precision (AP) resulting of 91.50%. After detecting the types of space use, the main research algorithm has been designed and coded, which includes determining the adjacency matrix of architectural plan spaces in seven stages. All research processes were conducted in Python, including dataset preparation, network object detection, and adjacency matrix algorithm design. Finally, the adjacency matrix is given to the input of the proposed plan generator network, which consequently, based on the resulting adjacency, obtains different placement modes for spaces and furniture.
基金Supported by the National Natural Science Foundation of China (70973104 and 11171304)the Zhejiang Natural Science Foundation of China (Y6110023)
文摘In this article, we introduce the Google＇s method for quality ranking of web page in a formal mathematical format, use the power iteration to improve the PageRank, and also discuss the effect of different q to the PageRank, as well as how a PageRank will be changed if more links are added to one page or removed from some pages.
文摘The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector <em>e<sub>j</sub></em> =(0, <span style="font-size:12.8px;white-space:normal;">…</span> , 1, … , 0)<sup>T</sup> and the all -1 vector <em>j</em> =(1, 1, <span style="font-size:12.8px;white-space:normal;">…</span>,1)<sup>T</sup>, the cosine of the (acute) angle formed by the vector <em>e<sub>j</sub></em> and the eigensubspace is called an angle of the graph. The cosine of the (acute) angle formed by the vector <em>j</em> and the eigensubspace is called a main angle of the graph. The angles and main angles are all important parameters on the graph, and they can be combined with the eigenvalues of the graph to determine the degree sequence of the graph, the number of triangles, quadrilaterals and pentagons on the graph, and the characteristic polynomials of the complement graph, but there is little study on the angles and main angles of the graph. In this paper, we determine the angles and main angles of the complete graph, the cube graph, the Petersen graph, the cycle and the complete bipartite graph.
基金supported by the National Key Research&Development Program of China(2020YFB0606404)National Natural Science Foundation of China(21908234)。
文摘Fischer-Tropsch synthesis(FTS)wax is a mixture of linear hydrocarbons with carbon number from C7 to C70+.Converting FTS wax into high-quality diesel(no sulfur and nitrogen contents)by hydrocracking technology is attractive in economy and practicability.Kinetic study of the hydrocracking of FTS wax in elementary step level is very challenging because of the huge amounts of reactions and species involved.Generation of reaction networks for hydrocracking of FTS wax in which the chain length goes up to C70 is described on the basis of Boolean adjacency matrixes.Each of the species(including paraffins,olefins and carbenium ions)involved in the elementary steps is represented digitally by using a(N+3)N matrix,in which a group of standardized numbering rules are designed to guarantee the unique identity of the species.Subsequently,the elementary steps are expressed by computer-aided matrix transformations in terms of proposed reaction rules.Dynamic memory allocation is used in species storage and a characteristic vector with nine elements is designed to store the key information of a(N+3)N matrix,which obviously reduces computer memory consumption and improves computing efficiency.The detailed reaction networks of FTS wax hydrocracking can be generated smoothly and accurately by the current method.The work is the basis of advanced elementary-step-level kinetic modeling.
基金National Natural Science Foundation of China under the Key Project under Grant Nos.10635040 and 60774073the Natural Science Foundation of Jiangsu Province of China under Grant No.BK2007075
文摘In this paper,based on the adjacency matrix of the network and its powers,the formulas are derived for theshortest path and the average path length,and an effective algorithm is presented.Furthermore,an example is providedto demonstrate the proposed method.
基金the National Natural Science Foundation of China(Grant No.51775473)the Natural Science Foundation of Hebei Province(Grant No.E2018203140).
文摘The mechanism of three⁃order Rubiks Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as the research object,and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC.In this paper,the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom,establishing a set of adjacency matrix,and determining the degree of freedom of the RC which is attributed to the number of non⁃zero elements in the set of adjacent matrix.The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC,which is simple and convenient for computer processing.The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science.Meanwhile,it is of great significance to the study of other complex mechanisms with variable degrees of freedom.
文摘The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.
文摘Technically, a group of more than two wheeled mobile robots working collectively towards a common goal are known as a multi-robot system. An increasing number of industries have implemented multi-robot systems to eliminate the risk of human injuries while working on hazardous tasks, and to improve productivity. Globally, engineers are continuously researching better, simple, and faster cooperative Control algorithms to provide a Control strategy where each agent in the robot formation can communicate effectively and achieve a consensus in their position, orientation and speed.<span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">This paper explores a novel Formation Building Algorithm and its global stability around a configuration vector. A simulation in MATLAB</span><sup><span style="font-size:12px;font-family:Verdana;"><span lang="ZH-CN" style="font-size:12pt;font-family:宋体;">?</span></span></sup><span style="font-family:Verdana;"> was carried out to examine the performance of the Algorithm for two geometric formations and a fixed number of robots. In addition, an obstacle avoidance technique was presented assuming that all robots are equipped with range sensors. In particular, a uniform rounded obstacle is used to analyze</span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">the performance of the technique with the use of detailed geometric calculations.</span>
文摘In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.
文摘The generating function for generating integer sequence of Aunu numbers of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator on the function for where the operation induces addition or subtraction on the pairs of ai, aj elements which are consecutive pairs of elements obtained from a generating set of some finite order. The paper identifies that the set of the generated pairs of integer sequence is non-associative. The paper also presents the graph theoretic applications of the integers generated in which subgraphs are deduced from the main graph and adjacency matrices and incidence matrices constructed. It was also established that some of the subgraphs were found to be regular graphs. The findings in this paper can further be used in coding theory, Boolean algebra and circuit designs.
