A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which...A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.展开更多
To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successf...To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.展开更多
A promising approach on the search for geometric constraint of directionalgraph in off-line parametric design has been put forward. The method for representation of thedirectional graph is given firstly, then the cons...A promising approach on the search for geometric constraint of directionalgraph in off-line parametric design has been put forward. The method for representation of thedirectional graph is given firstly, then the constraint model for every geometry element is putforward. By the search of geometric constraint, it sets up the topology constraint relation on thedifferent element objects, which are not related in geometry data base, and achieves the identifyfor the directional graph. The algorithm of recognizing geometric constraint is described in detail,in the meantime, the application example in off-line parametric design on dimension-driven isgiven.展开更多
Dear Editor,This letter considers the formation control of multiple mobile robot systems(MMRS)that only relies on the local observation information.A new distributed finite-time observer is proposed for MMRS under dir...Dear Editor,This letter considers the formation control of multiple mobile robot systems(MMRS)that only relies on the local observation information.A new distributed finite-time observer is proposed for MMRS under directed graph to estimate the relative information between each follower robot and the leader robot.Then the formation control problem is transformed into the tracking problem and a finite-time tracking controller is proposed based on the robot model feature.展开更多
Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback com...Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback combination of the agent's own state and neighbors' output,which can achieve exponential output consensus through intermittent communication. The controller is obtained by solving two linear matrix equations, and Zeno behavior is excluded.展开更多
Causality,the science of cause and effect,has made it possible to create a new family of models.Such models are often referred to as causal models.Unlike those of mathematical,numerical,empirical,or machine learning(M...Causality,the science of cause and effect,has made it possible to create a new family of models.Such models are often referred to as causal models.Unlike those of mathematical,numerical,empirical,or machine learning(ML)nature,causal models hope to tie the cause(s)to the effect(s)pertaining to a phenomenon(i.e.,data generating process)through causal principles.This paper presents one of the first works at creating causal models in the area of structural and construction engineering.To this end,this paper starts with a brief review of the principles of causality and then adopts four causal discovery algorithms,namely,PC(Peter-Clark),FCI(fast causal inference),GES(greedy equivalence search),and GRa SP(greedy relaxation of the sparsest permutation),have been used to examine four phenomena,including predicting the load-bearing capacity of axially loaded members,fire resistance of structural members,shear strength of beams,and resistance of walls against impulsive(blast)loading.Findings from this study reveal the possibility and merit of discovering complete and partial causal models.Finally,this study also proposes two simple metrics that can help assess the performance of causal discovery algorithms.展开更多
To protect user privacy and data security,the integration of Federated Learning(FL)and blockchain has become an emerging research hotspot.However,the limited throughput and high communication complexity of traditional...To protect user privacy and data security,the integration of Federated Learning(FL)and blockchain has become an emerging research hotspot.However,the limited throughput and high communication complexity of traditional blockchains limit their application in large-scale FL tasks,and the synchronous traditional FL will also reduce the training efficiency.To address these issues,in this paper,we propose a Directed Acyclic Graph(DAG)blockchain-enabled generalized Federated Dropout(FD)learning strategy,which could improve the efficiency of FL while ensuring the model generalization.Specifically,the DAG maintained by multiple edge servers will guarantee the security and traceability of the data,and the Reputation-based Tips Selection Algorithm(RTSA)is proposed to reduce the blockchain consensus delay.Second,the semi-asynchronous training among Intelligent Devices(IDs)is adopted to improve the training efficiency,and a reputation-based FD technology is proposed to prevent overfitting of the model.In addition,a Hybrid Optimal Resource Allocation(HORA)algorithm is introduced to minimize the network delay.Finally,simulation results demonstrate the effectiveness and superiority of the proposed algorithms.展开更多
The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. ...The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.展开更多
This paper presents an algorithm named the dependency-aware offloading framework(DeAOff),which is designed to optimize the deployment of Gen-AI decoder models in mobile edge computing(MEC)environments.These models,suc...This paper presents an algorithm named the dependency-aware offloading framework(DeAOff),which is designed to optimize the deployment of Gen-AI decoder models in mobile edge computing(MEC)environments.These models,such as decoders,pose significant challenges due to their interlayer dependencies and high computational demands,especially under edge resource constraints.To address these challenges,we propose a two-phase optimization algorithm that first handles dependencyaware task allocation and subsequently optimizes energy consumption.By modeling the inference process using directed acyclic graphs(DAGs)and applying constraint relaxation techniques,our approach effectively reduces execution latency and energy usage.Experimental results demonstrate that our method achieves a reduction of up to 20%in task completion time and approximately 30%savings in energy consumption compared to traditional methods.These outcomes underscore our solution’s robustness in managing complex sequential dependencies and dynamic MEC conditions,enhancing quality of service.Thus,our work presents a practical and efficient resource optimization strategy for deploying models in resourceconstrained MEC scenarios.展开更多
Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are...Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.展开更多
In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,ha...In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.展开更多
Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a majo...Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph （SDG） method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure （BCP） sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.展开更多
Qualitative algebraic equations are the basis of qualitative simulation,which are used to express the dynamic behavior of steady-state continuous processes.When the values and operation of qualitative variables are re...Qualitative algebraic equations are the basis of qualitative simulation,which are used to express the dynamic behavior of steady-state continuous processes.When the values and operation of qualitative variables are redefined,qualitative algebraic equations can be transformed into signed direct graphs,which are frequently used to predict the trend of dynamic changes.However,it is difficult to use traditional qualitative algebra methods based on artificial trial and error to solve a complex problem for dynamic trends.An important aspect of modern qualitative algebra is to model and characterize complex systems with the corresponding computer-aided automatic reasoning.In this study,a qualitative affection equation based on multiple conditions is proposed,which enables the signed di-rect graphs to describe complex systems better and improves the fault diagnosis resolution.The application to an industrial case shows that the method performs well.展开更多
In this paper we propose a novel model ＂recursive directed graph＂ based on feature structure, and apply it to represent the semantic relations of postpositive attributive structures in biomedical texts. The usages o...In this paper we propose a novel model ＂recursive directed graph＂ based on feature structure, and apply it to represent the semantic relations of postpositive attributive structures in biomedical texts. The usages of postpositive attributive are complex and variable, especially three categories： present participle phrase, past participle phrase, and preposition phrase as postpositire attributive, which always bring the difficulties of automatic parsing. We summarize these categories and annotate the semantic information. Compared with dependency structure, feature structure, being recursive directed graph, enhances semantic information extraction in biomedical field. The annotation results show that recursive directed graph is more suitable to extract complex semantic relations for biomedical text mining.展开更多
This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In thi...This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components Δ X, Δ Y and Δ Z sum up to zero.If the sum of the respective vector components ∑X,∑Y and ∑Z in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re_observed.After successful screening of errors by graph theory,network adjustment can be carried out.In this paper,the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.展开更多
To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the l...To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the large complex system model is defined using the directed graph model firstly, in which the nodes observing the fault by the hierarchical reconstruction of the directed graph are located, then the fault dependency matrix between these nodes and the fault sources are established. And then, we utilize the sensors' alarm probabilities under different situations to build the characteristic fault observation matrix in the fault observation space. Finally,the optimized corresponding diagnosis method using a fuzzy function, which describes the similarity between the actual observation vector and the fault's characteristic vector, is designed. The experimental results demonstrate that the proposed method can achieve high diagnosis efficiency and accuracy. It can be widely used in the real radar system.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
Based on the framework of support vector machines （SVM） using one-against-one （OAO） strategy, a new multi-class kernel method based on directed aeyclie graph （DAG） and probabilistic distance is proposed to raise...Based on the framework of support vector machines （SVM） using one-against-one （OAO） strategy, a new multi-class kernel method based on directed aeyclie graph （DAG） and probabilistic distance is proposed to raise the multi-class classification accuracies. The topology structure of DAG is constructed by rearranging the nodes＇ sequence in the graph. DAG is equivalent to guided operating SVM on a list, and the classification performance depends on the nodes＇ sequence in the graph. Jeffries-Matusita distance （JMD） is introduced to estimate the separability of each class, and the implementation list is initialized with all classes organized according to certain sequence in the list. To testify the effectiveness of the proposed method, numerical analysis is conducted on UCI data and hyperspectral data. Meanwhile, comparative studies using standard OAO and DAG classification methods are also conducted and the results illustrate better performance and higher accuracy of the orooosed JMD-DAG method.展开更多
Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-w...Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.展开更多
It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has...It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has been done when all variables are in a known directed acyclic graph(DAG). However, steady directed cyclic graphs(DCGs) may be involved when we simply combine modules containing local data together, where a module is composed of a child variable and its parent variables. So far, the physical and statistical meaning of steady DCGs remain unclear and unsolved. This paper illustrates the physical and statistical meaning of steady DCGs, and presents a method to calculate the JPD with local data, given that all variables are in a known single-valued Dynamic Uncertain Causality Graph(S-DUCG), and thus defines a new Bayesian Network with steady DCGs. The so-called single-valued means that only the causes of the true state of a variable are specified, while the false state is the complement of the true state.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12071260)。
文摘A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.
文摘To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.
基金This project is supported by National 863/C1MS Plan(No.863-511-507) Provincial Natural Science Foundation of Anhui, China (No.01042209).
文摘A promising approach on the search for geometric constraint of directionalgraph in off-line parametric design has been put forward. The method for representation of thedirectional graph is given firstly, then the constraint model for every geometry element is putforward. By the search of geometric constraint, it sets up the topology constraint relation on thedifferent element objects, which are not related in geometry data base, and achieves the identifyfor the directional graph. The algorithm of recognizing geometric constraint is described in detail,in the meantime, the application example in off-line parametric design on dimension-driven isgiven.
基金supported by the National Natural Science Foundation of China(62073113,62003122,62303148)the Fundamental Research Funds for the Central Universities(MCCSE2023A01,JZ2023HGTA0201,JZ2023HGQA0109)the Anhui Provincial Natural Science Foundation(2308085QF204)
文摘Dear Editor,This letter considers the formation control of multiple mobile robot systems(MMRS)that only relies on the local observation information.A new distributed finite-time observer is proposed for MMRS under directed graph to estimate the relative information between each follower robot and the leader robot.Then the formation control problem is transformed into the tracking problem and a finite-time tracking controller is proposed based on the robot model feature.
基金supported by the National Science and Technology Innovation 2030-Major Program(2022ZD 0115403)the National Natural Science Foundation of China(61991414)+1 种基金Chongqing Natural Science Foundation(CSTB2023NSCQJQX0018)Beijing Natural Science Foundation(L221005)
文摘Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback combination of the agent's own state and neighbors' output,which can achieve exponential output consensus through intermittent communication. The controller is obtained by solving two linear matrix equations, and Zeno behavior is excluded.
文摘Causality,the science of cause and effect,has made it possible to create a new family of models.Such models are often referred to as causal models.Unlike those of mathematical,numerical,empirical,or machine learning(ML)nature,causal models hope to tie the cause(s)to the effect(s)pertaining to a phenomenon(i.e.,data generating process)through causal principles.This paper presents one of the first works at creating causal models in the area of structural and construction engineering.To this end,this paper starts with a brief review of the principles of causality and then adopts four causal discovery algorithms,namely,PC(Peter-Clark),FCI(fast causal inference),GES(greedy equivalence search),and GRa SP(greedy relaxation of the sparsest permutation),have been used to examine four phenomena,including predicting the load-bearing capacity of axially loaded members,fire resistance of structural members,shear strength of beams,and resistance of walls against impulsive(blast)loading.Findings from this study reveal the possibility and merit of discovering complete and partial causal models.Finally,this study also proposes two simple metrics that can help assess the performance of causal discovery algorithms.
基金supported in part by the National Key R&D Program of China under Grant 2021YFB1714100in part by the National Natural Science Foundation of China(NSFC)under Grant 62371082 and 62001076in part by the Natural Science Foundation of Chongqing under Grant CSTB2023NSCQ-MSX0726 and cstc2020jcyjmsxmX0878.
文摘To protect user privacy and data security,the integration of Federated Learning(FL)and blockchain has become an emerging research hotspot.However,the limited throughput and high communication complexity of traditional blockchains limit their application in large-scale FL tasks,and the synchronous traditional FL will also reduce the training efficiency.To address these issues,in this paper,we propose a Directed Acyclic Graph(DAG)blockchain-enabled generalized Federated Dropout(FD)learning strategy,which could improve the efficiency of FL while ensuring the model generalization.Specifically,the DAG maintained by multiple edge servers will guarantee the security and traceability of the data,and the Reputation-based Tips Selection Algorithm(RTSA)is proposed to reduce the blockchain consensus delay.Second,the semi-asynchronous training among Intelligent Devices(IDs)is adopted to improve the training efficiency,and a reputation-based FD technology is proposed to prevent overfitting of the model.In addition,a Hybrid Optimal Resource Allocation(HORA)algorithm is introduced to minimize the network delay.Finally,simulation results demonstrate the effectiveness and superiority of the proposed algorithms.
文摘The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.
文摘This paper presents an algorithm named the dependency-aware offloading framework(DeAOff),which is designed to optimize the deployment of Gen-AI decoder models in mobile edge computing(MEC)environments.These models,such as decoders,pose significant challenges due to their interlayer dependencies and high computational demands,especially under edge resource constraints.To address these challenges,we propose a two-phase optimization algorithm that first handles dependencyaware task allocation and subsequently optimizes energy consumption.By modeling the inference process using directed acyclic graphs(DAGs)and applying constraint relaxation techniques,our approach effectively reduces execution latency and energy usage.Experimental results demonstrate that our method achieves a reduction of up to 20%in task completion time and approximately 30%savings in energy consumption compared to traditional methods.These outcomes underscore our solution’s robustness in managing complex sequential dependencies and dynamic MEC conditions,enhancing quality of service.Thus,our work presents a practical and efficient resource optimization strategy for deploying models in resourceconstrained MEC scenarios.
基金The National Natural Science Foundation of China(No.10971025)
文摘Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.
基金Supported by the Science and Technological Tackling Project of Heilongjiang Province(GB06A106)
文摘In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA110503-3)Fundamental Research Funds for the Central Universities of China(Grant No.2860219030)Foundation of Traction Power State Key Laboratory of Southwest Jiaotong University,China(Grant No.TPL1308)
文摘Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph （SDG） method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure （BCP） sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.
基金Supported by the National High Technology Research and Development Program of China(2009AA04Z133)
文摘Qualitative algebraic equations are the basis of qualitative simulation,which are used to express the dynamic behavior of steady-state continuous processes.When the values and operation of qualitative variables are redefined,qualitative algebraic equations can be transformed into signed direct graphs,which are frequently used to predict the trend of dynamic changes.However,it is difficult to use traditional qualitative algebra methods based on artificial trial and error to solve a complex problem for dynamic trends.An important aspect of modern qualitative algebra is to model and characterize complex systems with the corresponding computer-aided automatic reasoning.In this study,a qualitative affection equation based on multiple conditions is proposed,which enables the signed di-rect graphs to describe complex systems better and improves the fault diagnosis resolution.The application to an industrial case shows that the method performs well.
基金Supported by the National Natural Science Foundation of China(61202193,61202304)the Major Projects of Chinese National Social Science Foundation(11&ZD189)the Chinese Postdoctoral Science Foundation(2013M540593,2014T70722)
文摘In this paper we propose a novel model ＂recursive directed graph＂ based on feature structure, and apply it to represent the semantic relations of postpositive attributive structures in biomedical texts. The usages of postpositive attributive are complex and variable, especially three categories： present participle phrase, past participle phrase, and preposition phrase as postpositire attributive, which always bring the difficulties of automatic parsing. We summarize these categories and annotate the semantic information. Compared with dependency structure, feature structure, being recursive directed graph, enhances semantic information extraction in biomedical field. The annotation results show that recursive directed graph is more suitable to extract complex semantic relations for biomedical text mining.
文摘This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components Δ X, Δ Y and Δ Z sum up to zero.If the sum of the respective vector components ∑X,∑Y and ∑Z in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re_observed.After successful screening of errors by graph theory,network adjustment can be carried out.In this paper,the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.
基金the National Natural Science Foundation of China(No.61371024)the Aviation Science Fund of China(No.2013ZD53051)+1 种基金the IndustryAcademy-Research Project of Aviation Industry Corporation of China(No.cxy2013XGD14)the Space Support Technology Fund of China
文摘To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the large complex system model is defined using the directed graph model firstly, in which the nodes observing the fault by the hierarchical reconstruction of the directed graph are located, then the fault dependency matrix between these nodes and the fault sources are established. And then, we utilize the sensors' alarm probabilities under different situations to build the characteristic fault observation matrix in the fault observation space. Finally,the optimized corresponding diagnosis method using a fuzzy function, which describes the similarity between the actual observation vector and the fault's characteristic vector, is designed. The experimental results demonstrate that the proposed method can achieve high diagnosis efficiency and accuracy. It can be widely used in the real radar system.
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Sponsored by the National Natural Science Foundation of China(Grant No.61201310)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201160)the China Postdoctoral Science Foundation(Grant No.20110491067)
文摘Based on the framework of support vector machines （SVM） using one-against-one （OAO） strategy, a new multi-class kernel method based on directed aeyclie graph （DAG） and probabilistic distance is proposed to raise the multi-class classification accuracies. The topology structure of DAG is constructed by rearranging the nodes＇ sequence in the graph. DAG is equivalent to guided operating SVM on a list, and the classification performance depends on the nodes＇ sequence in the graph. Jeffries-Matusita distance （JMD） is introduced to estimate the separability of each class, and the implementation list is initialized with all classes organized according to certain sequence in the list. To testify the effectiveness of the proposed method, numerical analysis is conducted on UCI data and hyperspectral data. Meanwhile, comparative studies using standard OAO and DAG classification methods are also conducted and the results illustrate better performance and higher accuracy of the orooosed JMD-DAG method.
基金supported and funded by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2018R1D1A1B07049321).
文摘Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.
基金supported by the National Natural Science Foundation of China under Grant 71671103
文摘It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has been done when all variables are in a known directed acyclic graph(DAG). However, steady directed cyclic graphs(DCGs) may be involved when we simply combine modules containing local data together, where a module is composed of a child variable and its parent variables. So far, the physical and statistical meaning of steady DCGs remain unclear and unsolved. This paper illustrates the physical and statistical meaning of steady DCGs, and presents a method to calculate the JPD with local data, given that all variables are in a known single-valued Dynamic Uncertain Causality Graph(S-DUCG), and thus defines a new Bayesian Network with steady DCGs. The so-called single-valued means that only the causes of the true state of a variable are specified, while the false state is the complement of the true state.
