This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh ...This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.展开更多
Due to self-occlusion and high degree of freedom,estimating 3D hand pose from a single RGB image is a great challenging problem.Graph convolutional networks(GCNs)use graphs to describe the physical connection relation...Due to self-occlusion and high degree of freedom,estimating 3D hand pose from a single RGB image is a great challenging problem.Graph convolutional networks(GCNs)use graphs to describe the physical connection relationships between hand joints and improve the accuracy of 3D hand pose regression.However,GCNs cannot effectively describe the relationships between non-adjacent hand joints.Recently,hypergraph convolutional networks(HGCNs)have received much attention as they can describe multi-dimensional relationships between nodes through hyperedges;therefore,this paper proposes a framework for 3D hand pose estimation based on HGCN,which can better extract correlated relationships between adjacent and non-adjacent hand joints.To overcome the shortcomings of predefined hypergraph structures,a kind of dynamic hypergraph convolutional network is proposed,in which hyperedges are constructed dynamically based on hand joint feature similarity.To better explore the local semantic relationships between nodes,a kind of semantic dynamic hypergraph convolution is proposed.The proposed method is evaluated on publicly available benchmark datasets.Qualitative and quantitative experimental results both show that the proposed HGCN and improved methods for 3D hand pose estimation are better than GCN,and achieve state-of-the-art performance compared with existing methods.展开更多
This paper focuses on the problem of traffic flow forecasting,with the aim of forecasting future traffic conditions based on historical traffic data.This problem is typically tackled by utilizing spatio-temporal graph...This paper focuses on the problem of traffic flow forecasting,with the aim of forecasting future traffic conditions based on historical traffic data.This problem is typically tackled by utilizing spatio-temporal graph neural networks to model the intricate spatio-temporal correlations among traffic data.Although these methods have achieved performance improvements,they often suffer from the following limitations:These methods face challenges in modeling high-order correlations between nodes.These methods overlook the interactions between nodes at different scales.To tackle these issues,in this paper,we propose a novel model named multi-scale dynamic hypergraph convolutional network(MSDHGCN)for traffic flow forecasting.Our MSDHGCN can effectively model the dynamic higher-order relationships between nodes at multiple time scales,thereby enhancing the capability for traffic forecasting.Experiments on two real-world datasets demonstrate the effectiveness of the proposed method.展开更多
Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to cert...Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.展开更多
Complex networks play a crucial role in the study of collective behavior,encompassing the analysis of dynamical properties and network topology.In real-world systems,higher-order interactions among multiple entities a...Complex networks play a crucial role in the study of collective behavior,encompassing the analysis of dynamical properties and network topology.In real-world systems,higher-order interactions among multiple entities are widespread and significantly influence collective dynamics.Here,we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions.Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix.Furthermore,we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm.This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions.Our study provides new insights into dynamical optimization and topology tuning in hypergraphs,advancing the understanding of the interplay between higher-order interactions and collective dynamics.展开更多
Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important n...Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important nodes in a directed hypergraph.The algorithm introduces the Jaccard similarity of directed hypergraphs.By comparing the numbers of common neighbors between nodes with the total number of their neighbors,the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected,and can reflect the potential correlation between nodes.An improved susceptible–infected(SI)model in directed hypergraph is proposed,which considers nonlinear propagation mode and more realistic propagation mechanism.In addition,some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs.Finally,the ImPageRank algorithm is used to evaluate the performance of the SI model,network robustness and monotonicity.Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.展开更多
Hypergraphs,which encapsulate interactions of higher-order beyond mere pairwise connections,are essential for representing polyadic relationships within complex systems.Consequently,an increasing number of researchers...Hypergraphs,which encapsulate interactions of higher-order beyond mere pairwise connections,are essential for representing polyadic relationships within complex systems.Consequently,an increasing number of researchers are focusing on the centrality problem in hypergraphs.Specifically,researchers are tackling the challenge of utilizing higher-order structures to effectively define centrality metrics.This paper presents a novel approach,LGK,derived from the K-shell decomposition method,which incorporates both global and local perspectives.Empirical evaluations indicate that the LGK method provides several advantages,including reduced time complexity and improved accuracy in identifying critical nodes in hypergraphs.展开更多
Unlike traditional video cameras,event cameras capture asynchronous event streams in which each event encodes pixel location,triggers’timestamps,and the polarity of brightness changes.In this paper,we introduce a nov...Unlike traditional video cameras,event cameras capture asynchronous event streams in which each event encodes pixel location,triggers’timestamps,and the polarity of brightness changes.In this paper,we introduce a novel hypergraph-based framework for moving object classification.Specifically,we capture moving objects with an event camera,to perceive and collect asynchronous event streams in a high temporal resolution.Unlike stacked event frames,we encode asynchronous event data into a hypergraph,fully mining the high-order correlation of event data,and designing a mixed convolutional hypergraph neural network for training to achieve a more efficient and accurate motion target recognition.The experimental results show that our method has a good performance in moving object classification(e.g.,gait identification).展开更多
The rapid growth of marine applications leads to a significant increase in Maritime Devices(MDs).Traditional shore-based maritime communication networks face limitations,such as overloaded and transmission distance to...The rapid growth of marine applications leads to a significant increase in Maritime Devices(MDs).Traditional shore-based maritime communication networks face limitations,such as overloaded and transmission distance to provide network services for MDs.Unmanned Aerial Vehicles(UAVs)act as relays that can expand coverage and enhance the quality of service for offshore communication networks.We consider a multi-UAV-assisted Offshore Internet of Things(mUAV-OloT),and formulate a throughput maximization problem by jointly optimizing channel allocation,Leader MD(LMD)selection,UAV-LMD association,and LMD-MD association.Firstly,we propose the Hypergraph-based Two-Stage Matching(HTSM)algorithm where a Hypergraph-based LMD Selection(HLMDS)strategy is employed to identify the set of LMDs.Secondly,the Kuhn-Munkres algorithm is used to optimize the UAV-LMD association and a Weighted Threedimensional Hypergraph Matching(WTHM)algorithm is designed to solve the LMD-MD association and channel allocation.Numerical results show that the HTSM algorithm outperforms benchmark algorithms regarding throughput.展开更多
A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower tha...A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.展开更多
The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decompos...The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.展开更多
To overcome the limitation of the traditional clustering algorithms which fail to produce meaningful clusters in high-dimensional, sparseness and binary value data sets, a new method based on hypergraph model is propo...To overcome the limitation of the traditional clustering algorithms which fail to produce meaningful clusters in high-dimensional, sparseness and binary value data sets, a new method based on hypergraph model is proposed. The hypergraph model maps the relationship present in the original data in high dimensional space into a hypergraph. A hyperedge represents the similarity of attrlbute-value distribution between two points. A hypergraph partitioning algorithm is used to find a partitioning of the vertices such that the corresponding data items in each partition are highly related and the weight of the hyperedges cut by the partitioning is minimized. The quality of the clustering result can be evaluated by applying the intra-cluster singularity value. Analysis and experimental results have demonstrated that this approach is applicable and effective in wide ranging scheme.展开更多
This paper discusses the features and relevant theories of GIS spatial data model based on hypergraph,etc.The integrated concept model based on hypergraph and object_oriented model (HOOM) is proposed by the authors.Th...This paper discusses the features and relevant theories of GIS spatial data model based on hypergraph,etc.The integrated concept model based on hypergraph and object_oriented model (HOOM) is proposed by the authors.The principal contribution of this paper is that we study the K_section and other theories of hypergraph.An application example using HOOM is given at the end of the paper.展开更多
The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize...The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize functional confgurations using patent data.This study frst proposes a patent-data-driven PFC method based on a hypergraph network.It then constructs a weighted network model to optimize the combination of product function quantity and object from the perspective of big data,as follows:(1)The functional knowledge contained in the patent is extracted.(2)The functional hypergraph is constructed based on the co-occurrence relationship between patents and applicants.(3)The function and patent weight are calculated from the patent applicant’s perspective and patent value.(4)A weight calculation model of the PFC is developed.(5)The weighted frequent subgraph algorithm is used to obtain the optimal function combination list.This method is applied to an innovative design process of a bathroom shower.The results indicate that this method can help frms detach optimal function candidates and develop a multifunctional product.展开更多
In order to guarantee the wireless multicast throughput at a minimum cost, we propose a layered hypergraph high-dimension clustering algorithm (LayerHC) considering the channels and statistical locations of mobile mem...In order to guarantee the wireless multicast throughput at a minimum cost, we propose a layered hypergraph high-dimension clustering algorithm (LayerHC) considering the channels and statistical locations of mobile members. The algorithm can achieve a minimum multicast spanning tree to obtain a minimum number of relays and effective cooperative areas with low computational complexity.展开更多
Cloud storage has the characteristics of distributed and virtual, and it makes the ownership rights and management rights of users data separated. The master-slave architecture of cloud storage has a problem of single...Cloud storage has the characteristics of distributed and virtual, and it makes the ownership rights and management rights of users data separated. The master-slave architecture of cloud storage has a problem of single point failure. In this paper, we provide a cloud storage architecture model based on Semantic equivalence. According to semantic matching degree, this architecture divides the nodes into node cluster by creating semantic tree and maintains system routing through semantic hypergraph. Through simulation experiments show that dividing network into semantic can enhance scalability and flexibility of the system, and it can improve the efficiency of network organization and the security of cloud storage system, at the same time, it can also reduce the cloud data storage and the delay of reading time.展开更多
In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs...In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].展开更多
The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows：Dv（H）≤min{α≤（H）, p（H）, p（H）, T（H）}; De（H）≤min{v（H）, T...The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows：Dv（H）≤min{α≤（H）, p（H）, p（H）, T（H）}; De（H）≤min{v（H）, T（H）, p（H）}; DT（H） ≤αT（H）; S（H）≤ Dv （H） ＋ α（H）≤n; 2≤ Dv （H） ＋ T（H） ≤n; 2 〈 Dv （H） ＋ v（H）≤n/2 ＋ [n/r]; Dv （H） ＋ p（H） 〈_n;2≤De（H） ＋ Dv（H）≤n/2 ＋ [n/r];α（H） ＋ De（H）≤n;2 ≤ De（H） ＋ v（H）≤2[n/r]; 2 De（H） ＋ p（H）≤n-r ＋ 2.展开更多
It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is natu...It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.展开更多
基金Supported by Natural Science Foundation of HuBei Province(2022CFB299).
文摘This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.
基金the National Key Research and Development Program of China(No.2021ZD0111902)the National Natural Science Foundation of China(Nos.62172022 and U21B2038)。
文摘Due to self-occlusion and high degree of freedom,estimating 3D hand pose from a single RGB image is a great challenging problem.Graph convolutional networks(GCNs)use graphs to describe the physical connection relationships between hand joints and improve the accuracy of 3D hand pose regression.However,GCNs cannot effectively describe the relationships between non-adjacent hand joints.Recently,hypergraph convolutional networks(HGCNs)have received much attention as they can describe multi-dimensional relationships between nodes through hyperedges;therefore,this paper proposes a framework for 3D hand pose estimation based on HGCN,which can better extract correlated relationships between adjacent and non-adjacent hand joints.To overcome the shortcomings of predefined hypergraph structures,a kind of dynamic hypergraph convolutional network is proposed,in which hyperedges are constructed dynamically based on hand joint feature similarity.To better explore the local semantic relationships between nodes,a kind of semantic dynamic hypergraph convolution is proposed.The proposed method is evaluated on publicly available benchmark datasets.Qualitative and quantitative experimental results both show that the proposed HGCN and improved methods for 3D hand pose estimation are better than GCN,and achieve state-of-the-art performance compared with existing methods.
基金the National Key Research and Development Program of China(No.2021ZD0112400)。
文摘This paper focuses on the problem of traffic flow forecasting,with the aim of forecasting future traffic conditions based on historical traffic data.This problem is typically tackled by utilizing spatio-temporal graph neural networks to model the intricate spatio-temporal correlations among traffic data.Although these methods have achieved performance improvements,they often suffer from the following limitations:These methods face challenges in modeling high-order correlations between nodes.These methods overlook the interactions between nodes at different scales.To tackle these issues,in this paper,we propose a novel model named multi-scale dynamic hypergraph convolutional network(MSDHGCN)for traffic flow forecasting.Our MSDHGCN can effectively model the dynamic higher-order relationships between nodes at multiple time scales,thereby enhancing the capability for traffic forecasting.Experiments on two real-world datasets demonstrate the effectiveness of the proposed method.
基金Supported by the Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0884)。
文摘Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12247153,T2293771,and 12247101)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LTGY24A050002)+3 种基金the Sichuan Science and Technology Program(Grant Nos.2024NSFSC1364 and 2023NSFSC1919)the Project of Huzhou Science and Technology Bureau(Grant No.2022YZ29)the UESTCYDRI research start-up(Grant No.U03210066)the New Cornerstone Science Foundation through the Xplorer Prize。
文摘Complex networks play a crucial role in the study of collective behavior,encompassing the analysis of dynamical properties and network topology.In real-world systems,higher-order interactions among multiple entities are widespread and significantly influence collective dynamics.Here,we extend the synchronization alignment function framework to hypergraphs of arbitrary order by leveraging the multi-order Laplacian matrix to encode higher-order interactions.Our findings reveal that the upper bound of synchronous behavior is determined by the maximum eigenvalue of the multi-order Laplacian matrix.Furthermore,we decompose the contribution of each hyperedge to this eigenvalue and utilize it as a basis for designing an eigenvalue-based topology modification algorithm.This algorithm effectively enhances the upper bound of synchronous behavior without altering the total number of higher-order interactions.Our study provides new insights into dynamical optimization and topology tuning in hypergraphs,advancing the understanding of the interplay between higher-order interactions and collective dynamics.
基金Project supported by the National Natural Science Foundation of China(Grant No.62166010)the Guangxi Natural Science Foundation(Grant No.2023GXNSFAA026087).
文摘Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important nodes in a directed hypergraph.The algorithm introduces the Jaccard similarity of directed hypergraphs.By comparing the numbers of common neighbors between nodes with the total number of their neighbors,the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected,and can reflect the potential correlation between nodes.An improved susceptible–infected(SI)model in directed hypergraph is proposed,which considers nonlinear propagation mode and more realistic propagation mechanism.In addition,some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs.Finally,the ImPageRank algorithm is used to evaluate the performance of the SI model,network robustness and monotonicity.Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.
文摘Hypergraphs,which encapsulate interactions of higher-order beyond mere pairwise connections,are essential for representing polyadic relationships within complex systems.Consequently,an increasing number of researchers are focusing on the centrality problem in hypergraphs.Specifically,researchers are tackling the challenge of utilizing higher-order structures to effectively define centrality metrics.This paper presents a novel approach,LGK,derived from the K-shell decomposition method,which incorporates both global and local perspectives.Empirical evaluations indicate that the LGK method provides several advantages,including reduced time complexity and improved accuracy in identifying critical nodes in hypergraphs.
基金the National Key Research and Development Program of China(No.2021ZD0112400)。
文摘Unlike traditional video cameras,event cameras capture asynchronous event streams in which each event encodes pixel location,triggers’timestamps,and the polarity of brightness changes.In this paper,we introduce a novel hypergraph-based framework for moving object classification.Specifically,we capture moving objects with an event camera,to perceive and collect asynchronous event streams in a high temporal resolution.Unlike stacked event frames,we encode asynchronous event data into a hypergraph,fully mining the high-order correlation of event data,and designing a mixed convolutional hypergraph neural network for training to achieve a more efficient and accurate motion target recognition.The experimental results show that our method has a good performance in moving object classification(e.g.,gait identification).
基金supported by the National Natural Science Foundation of China(Nos.51939001,62371085,62122069,and 62071431)the Fundamental Research Funds for the Central Universities(No.3132023514)the FDCT-MOST Joint Project(No.0066/2019/AMJ).
文摘The rapid growth of marine applications leads to a significant increase in Maritime Devices(MDs).Traditional shore-based maritime communication networks face limitations,such as overloaded and transmission distance to provide network services for MDs.Unmanned Aerial Vehicles(UAVs)act as relays that can expand coverage and enhance the quality of service for offshore communication networks.We consider a multi-UAV-assisted Offshore Internet of Things(mUAV-OloT),and formulate a throughput maximization problem by jointly optimizing channel allocation,Leader MD(LMD)selection,UAV-LMD association,and LMD-MD association.Firstly,we propose the Hypergraph-based Two-Stage Matching(HTSM)algorithm where a Hypergraph-based LMD Selection(HLMDS)strategy is employed to identify the set of LMDs.Secondly,the Kuhn-Munkres algorithm is used to optimize the UAV-LMD association and a Weighted Threedimensional Hypergraph Matching(WTHM)algorithm is designed to solve the LMD-MD association and channel allocation.Numerical results show that the HTSM algorithm outperforms benchmark algorithms regarding throughput.
文摘A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.
基金Supported by the National Natural Science Foundation of China(Grant No.11161032)
文摘The problem of decomposing a complete 3-uniform hypergraph into Hamilton cycles was introduced by Bailey and Stevens using a generalization of Hamiltonian chain to uniform hypergraphs by Katona and Kierstead. Decomposing the complete 3-uniform hypergraphs Kn（3） into k-cycles （3 ≤ k 〈 n） was then considered by Meszka and Rosa. This study investigates this problem using a difference pattern of combinatorics and shows that Kn·5m（3） can be decomposed into 5-cycles for n ∈ {5, 7, 10, 11, 16, 17, 20, 22, 26} using computer programming.
文摘To overcome the limitation of the traditional clustering algorithms which fail to produce meaningful clusters in high-dimensional, sparseness and binary value data sets, a new method based on hypergraph model is proposed. The hypergraph model maps the relationship present in the original data in high dimensional space into a hypergraph. A hyperedge represents the similarity of attrlbute-value distribution between two points. A hypergraph partitioning algorithm is used to find a partitioning of the vertices such that the corresponding data items in each partition are highly related and the weight of the hyperedges cut by the partitioning is minimized. The quality of the clustering result can be evaluated by applying the intra-cluster singularity value. Analysis and experimental results have demonstrated that this approach is applicable and effective in wide ranging scheme.
文摘This paper discusses the features and relevant theories of GIS spatial data model based on hypergraph,etc.The integrated concept model based on hypergraph and object_oriented model (HOOM) is proposed by the authors.The principal contribution of this paper is that we study the K_section and other theories of hypergraph.An application example using HOOM is given at the end of the paper.
基金Supported by National Natural Science Foundation of China(Grant No.51875220)China Fujian Province Social Science Foundation Research Project(Grant No.FJ2021B128).
文摘The product functional confguration(PFC)is typically used by frms to satisfy the individual requirements of customers and is realized based on market analysis.This study aims to help frms analyze functions and realize functional confgurations using patent data.This study frst proposes a patent-data-driven PFC method based on a hypergraph network.It then constructs a weighted network model to optimize the combination of product function quantity and object from the perspective of big data,as follows:(1)The functional knowledge contained in the patent is extracted.(2)The functional hypergraph is constructed based on the co-occurrence relationship between patents and applicants.(3)The function and patent weight are calculated from the patent applicant’s perspective and patent value.(4)A weight calculation model of the PFC is developed.(5)The weighted frequent subgraph algorithm is used to obtain the optimal function combination list.This method is applied to an innovative design process of a bathroom shower.The results indicate that this method can help frms detach optimal function candidates and develop a multifunctional product.
基金Acknowledgements This work was supported by Natural Science Foundation of Beijing under Grant No. 4102041.
文摘In order to guarantee the wireless multicast throughput at a minimum cost, we propose a layered hypergraph high-dimension clustering algorithm (LayerHC) considering the channels and statistical locations of mobile members. The algorithm can achieve a minimum multicast spanning tree to obtain a minimum number of relays and effective cooperative areas with low computational complexity.
基金supported in part by the National Science and technology support program of China No. 2014BAH29F05the National High-Tech R&D Program (863 Program) No. 2015AA01A705+3 种基金the National Natural Science Foundation of China under Grant No. 61572072the National Science and Technology Major Project No. 2015ZX03001041the Fundamental Research Funds for the Central Universities No. FRF-TP-14-046A2"Research on the System of Personalized Education using Big Data"
文摘Cloud storage has the characteristics of distributed and virtual, and it makes the ownership rights and management rights of users data separated. The master-slave architecture of cloud storage has a problem of single point failure. In this paper, we provide a cloud storage architecture model based on Semantic equivalence. According to semantic matching degree, this architecture divides the nodes into node cluster by creating semantic tree and maintains system routing through semantic hypergraph. Through simulation experiments show that dividing network into semantic can enhance scalability and flexibility of the system, and it can improve the efficiency of network organization and the security of cloud storage system, at the same time, it can also reduce the cloud data storage and the delay of reading time.
基金Supported by the National Natural Science Foundation of China(Grant No.11601368)
文摘In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs Combin. 2007].
基金Supported by Ningbo Institute of Technology, Zhejiang Univ. Youth Innovation Foundation and Zhejiang Provincial Natural Science Foundation( Y604167).
文摘The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows：Dv（H）≤min{α≤（H）, p（H）, p（H）, T（H）}; De（H）≤min{v（H）, T（H）, p（H）}; DT（H） ≤αT（H）; S（H）≤ Dv （H） ＋ α（H）≤n; 2≤ Dv （H） ＋ T（H） ≤n; 2 〈 Dv （H） ＋ v（H）≤n/2 ＋ [n/r]; Dv （H） ＋ p（H） 〈_n;2≤De（H） ＋ Dv（H）≤n/2 ＋ [n/r];α（H） ＋ De（H）≤n;2 ≤ De（H） ＋ v（H）≤2[n/r]; 2 De（H） ＋ p（H）≤n-r ＋ 2.
基金Supported by NRF South Africathe National Natural Science Foundation of China(Grant No.11161032)
文摘It is proved in this paper that if G is a simple connected r-uniform hypergraph with ｜｜G｜｜≥2, then G has an edge e such that G - e - V1（e） is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.
