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
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
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
针对水下阵列波达方位(direction of arrival,DOA)估计在少快拍情况下对相邻声源分辨能力差的问题,提出了基于迭代原子范数最小化的均匀圆环阵DOA快速估计方法。所提方法利用模态域处理方法对阵列流形进行预处理,将均匀圆环阵转换为虚...针对水下阵列波达方位(direction of arrival,DOA)估计在少快拍情况下对相邻声源分辨能力差的问题,提出了基于迭代原子范数最小化的均匀圆环阵DOA快速估计方法。所提方法利用模态域处理方法对阵列流形进行预处理,将均匀圆环阵转换为虚拟直线阵,然后通过对角重构估计无噪接收信号协方差矩阵,消除模态域处理引入的非均匀噪声的影响。为了充分利用接收信号稀疏性,同时避免字典网格搜索带来的误差,在模态域引入迭代原子范数最小化稀疏恢复方法,提出均匀圆环阵迭代原子范数最小化(uniform circular array-iterative atomic norm minimization,UCA-IANM)方位估计方法。原子范数最小化稀疏恢复问题一般采用内点法求解,该方法随接收信号快拍数增加,计算量急剧上升,不适用于水下计算资源受限的场景。在交替方向乘子法(alternating direction multiplier method,ADMM)的基础上,针对正则化参数难以选择的问题,提出了基于参数优化ADMM的UCA-IANM(UCA-IANM assisted by ADMM with parameter optimization,UCA-IANM-APO)DOA快速估计算法。仿真实验与实测数据分析表明,UCA-IANM-APO DOA快速估计方法的角度分辨能力和估计精度均优于传统DOA估计方法,求解速度较内点法提升了两个数量级。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.
文摘针对水下阵列波达方位(direction of arrival,DOA)估计在少快拍情况下对相邻声源分辨能力差的问题,提出了基于迭代原子范数最小化的均匀圆环阵DOA快速估计方法。所提方法利用模态域处理方法对阵列流形进行预处理,将均匀圆环阵转换为虚拟直线阵,然后通过对角重构估计无噪接收信号协方差矩阵,消除模态域处理引入的非均匀噪声的影响。为了充分利用接收信号稀疏性,同时避免字典网格搜索带来的误差,在模态域引入迭代原子范数最小化稀疏恢复方法,提出均匀圆环阵迭代原子范数最小化(uniform circular array-iterative atomic norm minimization,UCA-IANM)方位估计方法。原子范数最小化稀疏恢复问题一般采用内点法求解,该方法随接收信号快拍数增加,计算量急剧上升,不适用于水下计算资源受限的场景。在交替方向乘子法(alternating direction multiplier method,ADMM)的基础上,针对正则化参数难以选择的问题,提出了基于参数优化ADMM的UCA-IANM(UCA-IANM assisted by ADMM with parameter optimization,UCA-IANM-APO)DOA快速估计算法。仿真实验与实测数据分析表明,UCA-IANM-APO DOA快速估计方法的角度分辨能力和估计精度均优于传统DOA估计方法,求解速度较内点法提升了两个数量级。
