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
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
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
We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G =...We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.展开更多
The problem of two-dimensional direction of arrival(2D-DOA)estimation for uniform planar arrays(UPAs)is investigated by employing the reduced-dimensional(RD)polynomial root finding technique and 2D multiple signal cla...The problem of two-dimensional direction of arrival(2D-DOA)estimation for uniform planar arrays(UPAs)is investigated by employing the reduced-dimensional(RD)polynomial root finding technique and 2D multiple signal classification(2D-MUSIC)algorithm.Specifically,based on the relationship between the noise subspace and steering vectors,we first construct 2D root polynomial for 2D-DOA estimates and then prove that the 2D polynomial function has infinitely many solutions.In particular,we propose a computationally efficient algorithm,termed RD-ROOT-MUSIC algorithm,to obtain the true solutions corresponding to targets by RD technique,where the 2D root-finding problem is substituted by two one-dimensional(1D)root-finding operations.Finally,accurate 2DDOA estimates can be obtained by a sample pairing approach.In addition,numerical simulation results are given to corroborate the advantages of the proposed algorithm.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
Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suf...Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.展开更多
New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous differ...New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.展开更多
In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider conn...In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ_r and ρ′_r and give a description of such hypergraphs.展开更多
Data-intensive computing is expected to be the next-generation IT computing paradigm. Data-intensive workflows in clouds are becoming more and more popular. How to schedule data-intensive workflow efficiently has beco...Data-intensive computing is expected to be the next-generation IT computing paradigm. Data-intensive workflows in clouds are becoming more and more popular. How to schedule data-intensive workflow efficiently has become the key issue. In this paper, first, we build a directed hypergraph model for data-intensive workflow, since Hypergraphs can more accurately model communication volume and better represent asymmetric problems, and the cut metric of hypergraphs is well suited for minimizing the total volume of communication.Second, we propose a concept data supportive ability to help the presentation of data-intensive workflow application and provide the merge operation details considering the data supportive ability. Third, we present an optimized hypergraph multi-level partitioning algorithm. Finally we bring a data reduced scheduling policy HEFT-P for data-intensive workflow. Through simulation,we compare HEFT-P with three typical workflow scheduling policies.The results indicate that HEFT-P could obtain reduced data scheduling and reduce the makespan of executing data-intensive展开更多
This paper proposes a novel algorithm for Two-Dimensional(2D) central Directionof-Arrival(DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform...This paper proposes a novel algorithm for Two-Dimensional(2D) central Directionof-Arrival(DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays(NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold(GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function.展开更多
单个较大非均匀超图聚类旨在将非均匀超图包含的节点划分为多个簇,使得同一簇内的节点更相似,而不同簇中的节点更不相似,具有广泛的应用场景。目前,最优的基于超图神经网络的非均匀超图聚类方法CIAH(co-cluster the interactions via at...单个较大非均匀超图聚类旨在将非均匀超图包含的节点划分为多个簇,使得同一簇内的节点更相似,而不同簇中的节点更不相似,具有广泛的应用场景。目前,最优的基于超图神经网络的非均匀超图聚类方法CIAH(co-cluster the interactions via attentive hypergraph neural network)虽然较好地学习了非均匀超图的关系信息,但仍存在两点不足:(1)对于局部关系信息的挖掘不足;(2)忽略了隐藏的高阶关系。因此,提出一种基于多尺度注意力和动态超图构建的非均匀超图聚类模型MADC(non-uniform hypergraph clustering combining multi-scale attention and dynamic construction)。一方面,使用多尺度注意力充分学习了超边中节点与节点之间的局部关系信息;另一方面,采用动态构建挖掘隐藏的高阶关系,进一步丰富了超图特征嵌入。真实数据集上的大量实验结果验证了MADC模型在非均匀超图聚类上的聚类准确率(accuracy,ACC)、标准互信息(normalized mutual information,NMI)和调整兰德指数(adjusted Rand index,ARI)均优于CIAH等所有Baseline方法。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.
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.
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.
文摘We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph G<sup>k</sup>. For the k-uniform hypergraph G<sup>k</sup> underlying a non-complete graph G = (V, E), its rupture degree r(G<sup>k</sup>) is defined as r(G<sup>k</sup>) = max{ω(G<sup>k</sup> - X) - |X| - m(G<sup>k</sup> - X): X <span style="white-space:nowrap;">⊂ V(G<sup>k</sup>), ω(G<sup>k</sup> - X) > 1}, where X is a cut set (or destruction strategy) of G<sup>k</sup>, ω(G<sup>k</sup> - X) and m(G<sup>k</sup> - X) denote the number of components and the order of a largest component in G<sup>k</sup> - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.
基金supported by the National Natural Science Foundation of China(Nos.61631020,61971218,61601167,61371169)。
文摘The problem of two-dimensional direction of arrival(2D-DOA)estimation for uniform planar arrays(UPAs)is investigated by employing the reduced-dimensional(RD)polynomial root finding technique and 2D multiple signal classification(2D-MUSIC)algorithm.Specifically,based on the relationship between the noise subspace and steering vectors,we first construct 2D root polynomial for 2D-DOA estimates and then prove that the 2D polynomial function has infinitely many solutions.In particular,we propose a computationally efficient algorithm,termed RD-ROOT-MUSIC algorithm,to obtain the true solutions corresponding to targets by RD technique,where the 2D root-finding problem is substituted by two one-dimensional(1D)root-finding operations.Finally,accurate 2DDOA estimates can be obtained by a sample pairing approach.In addition,numerical simulation results are given to corroborate the advantages of the proposed algorithm.
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National Natural Science Foundation of China(61973037)National 173 Program Project(2019-JCJQ-ZD-324)。
文摘Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.
文摘New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.
基金Supported by the National Natural Science Foundation of China(Grant Nos.116013681140143411771322)
文摘In this paper, we set ρ_r =~r4^（1/2） and ρ′_r= β^（-1/r）, where β =-1/6 ·（100 ＋ 12·（69）^（1/2））^（1/3）-2/（3·（100＋12·（69）^（1/2）））^（1/3）＋4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ_r and ρ′_r and give a description of such hypergraphs.
文摘Data-intensive computing is expected to be the next-generation IT computing paradigm. Data-intensive workflows in clouds are becoming more and more popular. How to schedule data-intensive workflow efficiently has become the key issue. In this paper, first, we build a directed hypergraph model for data-intensive workflow, since Hypergraphs can more accurately model communication volume and better represent asymmetric problems, and the cut metric of hypergraphs is well suited for minimizing the total volume of communication.Second, we propose a concept data supportive ability to help the presentation of data-intensive workflow application and provide the merge operation details considering the data supportive ability. Third, we present an optimized hypergraph multi-level partitioning algorithm. Finally we bring a data reduced scheduling policy HEFT-P for data-intensive workflow. Through simulation,we compare HEFT-P with three typical workflow scheduling policies.The results indicate that HEFT-P could obtain reduced data scheduling and reduce the makespan of executing data-intensive
基金supported by the National Natural Science Foundation of China(No.61401513)
文摘This paper proposes a novel algorithm for Two-Dimensional(2D) central Directionof-Arrival(DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays(NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold(GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function.
