Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult si...Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.展开更多
Surface observations and CHAMP measurement data are employed to develop a three-dimensional surface spline(3DSS)model of China's Mainland.The magnetic field distribution at the satellite level is then demonstrated...Surface observations and CHAMP measurement data are employed to develop a three-dimensional surface spline(3DSS)model of China's Mainland.The magnetic field distribution at the satellite level is then demonstrated using the model obtained.The results of this model are compared and verifi ed by deriving the corresponding two(2DTY)and threedimensional(3DTY)Taylor polynomial models.Issues such as the removal of disruptive geomagnetic fi elds,the data gap between the surface and satellite levels,and boundary eff ects are carefully considered during modeling.We then focus on evaluating the modeling eff ect of the satellite data.Ten satellite points not involved in the modeling procedure are selected,and the residuals,absolute change rates,and RMSEs of these points are calculated.Results show that the distribution of the magnetic fi eld determined by the 3DSS model is highly consistent with that obtained from the IGRF12 model.Expect for component Y,the absolute change rates of other components are less than 0.5%.Specifi cally,the RMSE of Y of 3DSS is nearly 60%lower than those of 3DTY and 2DTY;the RMSE of other components of the former are also over 90%lower than those of the latter.This fi nding implies that the 3DSS model has good performance for modeling satellite data and its results are reliable.Moreover,the modeling eff ect of 3DTY is better than that of 2DTY.展开更多
Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, ...Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix A is called monotone if A is transitive or A is monotone increasing. In this paper, the convergence of monotone matrices is studied. The results obtained here develop the corresponding ones on lattice matrices shown in the references.展开更多
The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating se...The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating set(Min SDS) problem in a multi-agent system.We design a game framework for SDS and show that every Nash equilibrium(NE) is a minimal SDS,which is also a Pareto-optimal solution.We prove that the proposed game is an exact potential game,and thus NE exists,and design a polynomial-time distributed local algorithm which converges to an NE in O(n) rounds of interactions.Extensive experiments are done to test the performance of our algorithm,and some interesting phenomena are witnessed.展开更多
When dealing with the ratings from users,traditional collaborative filtering algorithms do not consider the credibility of rating data,which affects the accuracy of similarity.To address this issue,the paper proposes ...When dealing with the ratings from users,traditional collaborative filtering algorithms do not consider the credibility of rating data,which affects the accuracy of similarity.To address this issue,the paper proposes an improved algorithm based on classification and user trust.It firstly classifies all the ratings by the categories of items.And then,for each category,it evaluates the trustworthy degree of each user on the category and imposes the degree on the ratings of the user.Finally,the algorithm explores the similarities between users,finds the nearest neighbors,and makes recommendations within each category.Simulations show that the improved algorithm outperforms the traditional collaborative filtering algorithms and enhances the accuracy of recommendation.展开更多
This paper presents the theoretical results on the master-slave(or driving-response) synchronization of two memristive neural networks in the presence of additive noise. First,a control law with a linear time-delay fe...This paper presents the theoretical results on the master-slave(or driving-response) synchronization of two memristive neural networks in the presence of additive noise. First,a control law with a linear time-delay feedback term and a discontinuous feedback term is introduced. By utilizing the stability theory of stochastic differential equations, sufficient conditions are derived for ascertaining global synchronization in mean square using this control law. Second, an adaptive control law consisting of a linear feedback term and a discontinuous feedback term is designed to achieve global synchronization in mean square, and it does not need prior information of network parameters or random disturbances. Finally, simulation results are presented to substantiate the theoretical results.展开更多
In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. ...In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. in general, a negative answer. Therefore, our question is for what kind of labeled graphs G each partial totally non-positive matrix whose associated graph is G has a totally non-positive completion? If G is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion.展开更多
Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted n...Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.展开更多
Network representation learning plays an important role in the field of network data mining. By embedding network structures and other features into the representation vector space of low dimensions, network represent...Network representation learning plays an important role in the field of network data mining. By embedding network structures and other features into the representation vector space of low dimensions, network representation learning algorithms can provide high-quality feature input for subsequent tasks, such as network link prediction, network vertex classification, and network visualization. The existing network representation learning algorithms can be trained based on the structural features, vertex texts, vertex tags, community information, etc.However, there exists a lack of algorithm of using the future evolution results of the networks to guide the network representation learning. Therefore, this paper aims at modeling the future network evolution results of the networks based on the link prediction algorithm, introducing the future link probabilities between vertices without edges into the network representation learning tasks. In order to make the network representation vectors contain more feature factors, the text features of the vertices are also embedded into the network representation vectors. Based on the above two optimization approaches, we propose a novel network representation learning algorithm, Network Representation learning algorithm based on the joint optimization of Three Features(TFNR). Based on Inductive Matrix Completion(IMC), TFNR algorithm introduces the future probabilities between vertices without edges and text features into the procedure of modeling network structures, which can avoid the problem of the network structure sparse. Experimental results show that the proposed TFNR algorithm performs well in network vertex classification and visualization tasks on three real citation network datasets.展开更多
The uniqueness of meromorphic functions that share four values is investigated. A necessary condition to the case is acquired, and some partial results for question'1CM+3IM=4CM' are obtained.
In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ (Rn) to the Lebesgue space Lp(Rn) for 1<p<∞ and 0 < γ < min{ n/2 ,...In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ (Rn) to the Lebesgue space Lp(Rn) for 1<p<∞ and 0 < γ < min{ n/2 , n/p }.展开更多
The performances of semisupervised clustering for unlabeled data are often superior to those of unsupervised learning,which indicates that semantic information attached to clusters can significantly improve feature re...The performances of semisupervised clustering for unlabeled data are often superior to those of unsupervised learning,which indicates that semantic information attached to clusters can significantly improve feature representation capability.In a graph convolutional network(GCN),each node contains information about itself and its neighbors that is beneficial to common and unique features among samples.Combining these findings,we propose a deep clustering method based on GCN and semantic feature guidance(GFDC) in which a deep convolutional network is used as a feature generator,and a GCN with a softmax layer performs clustering assignment.First,the diversity and amount of input information are enhanced to generate highly useful representations for downstream tasks.Subsequently,the topological graph is constructed to express the spatial relationship of features.For a pair of datasets,feature correspondence constraints are used to regularize clustering loss,and clustering outputs are iteratively optimized.Three external evaluation indicators,i.e.,clustering accuracy,normalized mutual information,and the adjusted Rand index,and an internal indicator,i.e., the Davidson-Bouldin index(DBI),are employed to evaluate clustering performances.Experimental results on eight public datasets show that the GFDC algorithm is significantly better than the majority of competitive clustering methods,i.e.,its clustering accuracy is20% higher than the best clustering method on the United States Postal Service dataset.The GFDC algorithm also has the highest accuracy on the smaller Amazon and Caltech datasets.Moreover,DBI indicates the dispersion of cluster distribution and compactness within the cluster.展开更多
Owing to the explosive growth of Internet traffic, network operators must be able to monitor the entire network situation and efficiently manage their network resources. Traditional network analysis methods that usual...Owing to the explosive growth of Internet traffic, network operators must be able to monitor the entire network situation and efficiently manage their network resources. Traditional network analysis methods that usually work on a single machine are no longer suitable for huge traffic data owing to their poor processing ability. Big data frameworks, such as Hadoop and Spark, can handle such analysis jobs even for a large amount of network traffic.However, Hadoop and Spark are inherently designed for offline data analysis. To cope with streaming data, various stream-processing-based frameworks have been proposed, such as Storm, Flink, and Spark Streaming. In this study, we propose an online Internet traffic monitoring system based on Spark Streaming. The system comprises three parts, namely, the collector, messaging system, and stream processor. We considered the TCP performance monitoring as a special use case of showing how network monitoring can be performed with our proposed system.We conducted typical experiments with a cluster in standalone mode, which showed that our system performs well for large Internet traffic measurement and monitoring.展开更多
基金supported in part by the 2023 Schoollevel Education and Teaching Reform Project of Guangdong Ocean University。
文摘Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.
基金This work was supported by the National Natural Science Foundation of China(Nos.41974073,41404053)Special Project for Meteo-Scientifi c Research in the Public Interest(No.GYHY201306073)。
文摘Surface observations and CHAMP measurement data are employed to develop a three-dimensional surface spline(3DSS)model of China's Mainland.The magnetic field distribution at the satellite level is then demonstrated using the model obtained.The results of this model are compared and verifi ed by deriving the corresponding two(2DTY)and threedimensional(3DTY)Taylor polynomial models.Issues such as the removal of disruptive geomagnetic fi elds,the data gap between the surface and satellite levels,and boundary eff ects are carefully considered during modeling.We then focus on evaluating the modeling eff ect of the satellite data.Ten satellite points not involved in the modeling procedure are selected,and the residuals,absolute change rates,and RMSEs of these points are calculated.Results show that the distribution of the magnetic fi eld determined by the 3DSS model is highly consistent with that obtained from the IGRF12 model.Expect for component Y,the absolute change rates of other components are less than 0.5%.Specifi cally,the RMSE of Y of 3DSS is nearly 60%lower than those of 3DTY and 2DTY;the RMSE of other components of the former are also over 90%lower than those of the latter.This fi nding implies that the 3DSS model has good performance for modeling satellite data and its results are reliable.Moreover,the modeling eff ect of 3DTY is better than that of 2DTY.
文摘Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix A is called monotone if A is transitive or A is monotone increasing. In this paper, the convergence of monotone matrices is studied. The results obtained here develop the corresponding ones on lattice matrices shown in the references.
基金supported in part by the National Natural Science Foundation of China(U20A2068, 11771013)Zhejiang Provincial Natural Science Foundation of China (LD19A010001)。
文摘The secure dominating set(SDS),a variant of the dominating set,is an important combinatorial structure used in wireless networks.In this paper,we apply algorithmic game theory to study the minimum secure dominating set(Min SDS) problem in a multi-agent system.We design a game framework for SDS and show that every Nash equilibrium(NE) is a minimal SDS,which is also a Pareto-optimal solution.We prove that the proposed game is an exact potential game,and thus NE exists,and design a polynomial-time distributed local algorithm which converges to an NE in O(n) rounds of interactions.Extensive experiments are done to test the performance of our algorithm,and some interesting phenomena are witnessed.
基金supported by Phase 4,Software Engineering(Software Service Engineering)under Grant No.XXKZD1301
文摘When dealing with the ratings from users,traditional collaborative filtering algorithms do not consider the credibility of rating data,which affects the accuracy of similarity.To address this issue,the paper proposes an improved algorithm based on classification and user trust.It firstly classifies all the ratings by the categories of items.And then,for each category,it evaluates the trustworthy degree of each user on the category and imposes the degree on the ratings of the user.Finally,the algorithm explores the similarities between users,finds the nearest neighbors,and makes recommendations within each category.Simulations show that the improved algorithm outperforms the traditional collaborative filtering algorithms and enhances the accuracy of recommendation.
基金supported by the Research Grants Council of the Hong Kong Special Administrative Region,China(416811,416812)National Natural Science Foundation of China(61573003)part by the Scientific Research Fund of Hunan Provincial Education Department of China(15k026)
文摘This paper presents the theoretical results on the master-slave(or driving-response) synchronization of two memristive neural networks in the presence of additive noise. First,a control law with a linear time-delay feedback term and a discontinuous feedback term is introduced. By utilizing the stability theory of stochastic differential equations, sufficient conditions are derived for ascertaining global synchronization in mean square using this control law. Second, an adaptive control law consisting of a linear feedback term and a discontinuous feedback term is designed to achieve global synchronization in mean square, and it does not need prior information of network parameters or random disturbances. Finally, simulation results are presented to substantiate the theoretical results.
基金The work was supported by the National Science Foundation of China (10571146).
文摘In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. in general, a negative answer. Therefore, our question is for what kind of labeled graphs G each partial totally non-positive matrix whose associated graph is G has a totally non-positive completion? If G is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion.
基金partly supported by the National Natural Science Foundation of China(61751303,U20A2068,11771013)the Zhejiang Provincial Natural Science Foundation of China(LD19A010001)the Fundamental Research Funds for the Central Universities。
文摘Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.
文摘Network representation learning plays an important role in the field of network data mining. By embedding network structures and other features into the representation vector space of low dimensions, network representation learning algorithms can provide high-quality feature input for subsequent tasks, such as network link prediction, network vertex classification, and network visualization. The existing network representation learning algorithms can be trained based on the structural features, vertex texts, vertex tags, community information, etc.However, there exists a lack of algorithm of using the future evolution results of the networks to guide the network representation learning. Therefore, this paper aims at modeling the future network evolution results of the networks based on the link prediction algorithm, introducing the future link probabilities between vertices without edges into the network representation learning tasks. In order to make the network representation vectors contain more feature factors, the text features of the vertices are also embedded into the network representation vectors. Based on the above two optimization approaches, we propose a novel network representation learning algorithm, Network Representation learning algorithm based on the joint optimization of Three Features(TFNR). Based on Inductive Matrix Completion(IMC), TFNR algorithm introduces the future probabilities between vertices without edges and text features into the procedure of modeling network structures, which can avoid the problem of the network structure sparse. Experimental results show that the proposed TFNR algorithm performs well in network vertex classification and visualization tasks on three real citation network datasets.
基金Project supported by the National Natural Science Foundation of China(19971052) and the Programme of Hunan Education Foundation(02C095)
文摘The uniqueness of meromorphic functions that share four values is investigated. A necessary condition to the case is acquired, and some partial results for question'1CM+3IM=4CM' are obtained.
基金supported by the National Natural Science Foundation of China under Grant No.11626165the School Young Foundation of Taiyuan University of Technology under Grant No.2015QN062the Natural Science Foundation of Shanxi Province under Grant No.201701D221013
基金supported by National Natural Science Foundation of China (Grant No. 10901017)Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574) +3 种基金the Fundamental Research Funds for the Central Universitiessupported by National Natural Science Foundation of China (Grant No. 10931001)the Research Fund for the Dectoral Program of Higher Education of China (Grant No. 20090003110018)Program for Changjiang Scholars and Innovative Research Team in University of China
文摘In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ (Rn) to the Lebesgue space Lp(Rn) for 1<p<∞ and 0 < γ < min{ n/2 , n/p }.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10931001, 10901017） and Specialized Research Fund for the Doctoral Program of China （Grant No. 20090003110018）Acknowledgements The authors would like to express their gratitude to the referee for his/her very careful reading and many important valuable comments.
文摘在这份报纸，作者给整流器的固定[b，，] 从同类的 Sobolev 空间[(L)\dot ] g p (\mathbbRn )\dot L_\gamma ^ p \left ({\mathbb { R }^ n }\right ) 到 Lebesgue 空间 L p (吗？n ) 为 1 < p < ，表示 Marcinkiewicz 积分，不平的 hypersingular 核由 $\mu _ 定义 {\Omega， \gamma } f\left (x \right )=\left ({\int_0 ^\infty {\left |{\int_{\left |{ x - y }\right |\leqslant t }{\frac {{\Omega \left ({ x - y }\right )}}{{\left |{ x - y }\right|^{ n - 1 }}} f\left ( y \right ) dy }}\right|^ 2 \frac {{ dt }}{{ t ^{ 3 + 2 \gamma }}}}} \right )^{ \frac { 1 }{ 2 }}， $\mu _{ \Omega ， \gamma } f\left ( x \right )= \left ({ \int_0 ^ \infty { \left |{\int_{\left |{ x - y }\right |\leqslant t }{\frac {{\Omega \left ({ x - y }\right )}}{{\left |{ x - y }\right|^{ n - 1 }}} f\left ( y \right ) dy }}\right|^ 2 \frac {{ dt }}{{ t ^{ 3 + 2 \gamma }}}}} \right )^{ \frac { 1 }{ 2 }}，
基金supported by the Hebei Province Introduction of Studying Abroad Talent Funded Project (No. C20200302)the Opening Fund of Hebei Key Laboratory of Machine Learning and Computational Intelligence (Nos. 2019-2021-A and ZZ201909-202109-1)+1 种基金the National Natural Science Foundation of China (No. 61976141)the Social Science Foundation of Hebei Province (No. HB20TQ005)。
文摘The performances of semisupervised clustering for unlabeled data are often superior to those of unsupervised learning,which indicates that semantic information attached to clusters can significantly improve feature representation capability.In a graph convolutional network(GCN),each node contains information about itself and its neighbors that is beneficial to common and unique features among samples.Combining these findings,we propose a deep clustering method based on GCN and semantic feature guidance(GFDC) in which a deep convolutional network is used as a feature generator,and a GCN with a softmax layer performs clustering assignment.First,the diversity and amount of input information are enhanced to generate highly useful representations for downstream tasks.Subsequently,the topological graph is constructed to express the spatial relationship of features.For a pair of datasets,feature correspondence constraints are used to regularize clustering loss,and clustering outputs are iteratively optimized.Three external evaluation indicators,i.e.,clustering accuracy,normalized mutual information,and the adjusted Rand index,and an internal indicator,i.e., the Davidson-Bouldin index(DBI),are employed to evaluate clustering performances.Experimental results on eight public datasets show that the GFDC algorithm is significantly better than the majority of competitive clustering methods,i.e.,its clustering accuracy is20% higher than the best clustering method on the United States Postal Service dataset.The GFDC algorithm also has the highest accuracy on the smaller Amazon and Caltech datasets.Moreover,DBI indicates the dispersion of cluster distribution and compactness within the cluster.
基金partially supported by Grant-in-Aid for Scientific Research from Japan Society for Promotion of Science(JSPS)Qinghai Joint Research Grant(No.2016-HZ-804)Research Collaboration Grant from NII,Japan
文摘Owing to the explosive growth of Internet traffic, network operators must be able to monitor the entire network situation and efficiently manage their network resources. Traditional network analysis methods that usually work on a single machine are no longer suitable for huge traffic data owing to their poor processing ability. Big data frameworks, such as Hadoop and Spark, can handle such analysis jobs even for a large amount of network traffic.However, Hadoop and Spark are inherently designed for offline data analysis. To cope with streaming data, various stream-processing-based frameworks have been proposed, such as Storm, Flink, and Spark Streaming. In this study, we propose an online Internet traffic monitoring system based on Spark Streaming. The system comprises three parts, namely, the collector, messaging system, and stream processor. We considered the TCP performance monitoring as a special use case of showing how network monitoring can be performed with our proposed system.We conducted typical experiments with a cluster in standalone mode, which showed that our system performs well for large Internet traffic measurement and monitoring.
