The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar ...The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this note,we completely characterize the semipotent rings whose unit graphs are planar.As a consequence,we list all semilocal rings with planar unit graphs.展开更多
Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.I...Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.In this paper,we investigate the Wiener index and hyper-Wiener index of G(R)and explicitly determine their values.展开更多
This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, mod...This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, modified cutwidth, and bandwidth sum(linear arrangement).展开更多
The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless n...The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless networks.Investigation of some properties of independent set(IS)in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms.Several constant factor approximation algorithms are presented for the CDS problem in UDGs.Simulation results show that the proposed algorithms perform better than some known ones.展开更多
微表情检测旨在视频中定位幅度微弱、时间短暂的表情区间。其难点在于有效提取面部区域间的动态关联特征和多尺度时序特征,进而精准捕捉面部各区域微小动作之间的关联。针对这些问题,提出了一种融合自适应图注意力和多尺度可变空洞卷积...微表情检测旨在视频中定位幅度微弱、时间短暂的表情区间。其难点在于有效提取面部区域间的动态关联特征和多尺度时序特征,进而精准捕捉面部各区域微小动作之间的关联。针对这些问题,提出了一种融合自适应图注意力和多尺度可变空洞卷积的微表情检测网络(AG-DDNet)。通过引入参数可学习矩阵来实现键值对的特征变换,通过计算面部区域特征向量间的相似度得到动态邻接矩阵,并结合图注意力机制计算区域间权重系数,实现特征的动态融合;采用了多尺度可变空洞卷积模块,通过自适应池化与卷积组合的预测器生成动态感受野,从而实现多尺度的特征提取;引入基于Fisher信息矩阵的自然梯度优化机制,通过Fisher Adam优化器有效捕捉参数空间的几何结构信息,实现学习率的精确自适应调整,从而显著增强了模型对微表情和宏表情的协同检测能力。在微表情检测任务中,该算法与同类代表性算法相比,在CAS(ME)2数据集和SAMM Long Videos数据集上的性能分别提升了54.20%和20.11%。与最新算法相比,两个数据集上的提升幅度分别为38.43%和6.81%,有效证明了该方法在长视频微表情检测任务上的优越性能。展开更多
The sustainability of the Internet of Things(IoT)involves various issues,such as poor connectivity,scalability problems,interoperability issues,and energy inefficiency.Although the Sixth Generation of mobile networks(...The sustainability of the Internet of Things(IoT)involves various issues,such as poor connectivity,scalability problems,interoperability issues,and energy inefficiency.Although the Sixth Generation of mobile networks(6G)allows for Ultra-Reliable Low-Latency Communication(URLLC),enhanced Mobile Broadband(eMBB),and massive Machine-Type Communications(mMTC)services,it faces deployment challenges such as the short range of sub-THz and THz frequency bands,low capability to penetrate obstacles,and very high path loss.This paper presents a network architecture to enhance the connectivity of wireless IoT mesh networks that employ both 6G and Wi-Fi technologies.In this architecture,local communications are carried through the mesh network,which uses a virtual backbone to relay packets to local nodes,while remote communications are carried through the 6G network.The virtual backbone is created using a heuristic distributed ConnectedDominating Set(CDS)algorithm.In this algorithm,each node uses information collected from its one-and two-hop neighbors to determine its role and find the set of expansion nodes that are used to select the next CDS nodes.The proposed algorithm has O(n)message and O(K)time complexities,where n is the number of nodes in the network,and K is the depth of the cluster.The study proved that the approximation ratio of the algorithmhas an upper bound of 2.06748(3.4306MCDS+4.8185).Performance evaluations compared the size of the CDS against the theoretical limit and recent CDS clustering algorithms.Results indicate that the proposed algorithm has the smallest average slope for the size of the CDS as the number of nodes increases.展开更多
In this paper, the automorphism group is completely determined, of the unitary Cayley graph, the unit graph and the total graph, over the ring of Gaussian integers modulo a prime power.
Let T be the subgroup of the multiplicative group C^(×)consisting of all complex numbers z with|z|=1.A T-gain graph is a tripleΦ=(G,T,φ)(or short for(G,φ))consisting of a simple graph G=(V,E),as the underlying...Let T be the subgroup of the multiplicative group C^(×)consisting of all complex numbers z with|z|=1.A T-gain graph is a tripleΦ=(G,T,φ)(or short for(G,φ))consisting of a simple graph G=(V,E),as the underlying graph of(G,Φ),the circle group T and a gain functionΦ:→E→T such that φ(vivj)=φ(vjvi) for any adjacent vertices vi and vj.Let i+(G,φ)(resp.,i+(G))be the positive inertia index of(G,φ)(resp.,G).In this paper,we prove that-c(G)≤i+(G,φ)-i+(G)≤c(G),where c(G)is the cyclomatic number of G,and characterize all the corresponding extremal graphs.展开更多
基金supported by the National Natural Science Foundation of China(11661013,11661014,11961050)Guangxi Natural Science Foundation(2016GXNSFCA380014,2016GXNSFDA380017).
文摘The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this note,we completely characterize the semipotent rings whose unit graphs are planar.As a consequence,we list all semilocal rings with planar unit graphs.
基金supported in part by a grant from Science and Engineering Research Board,India(Ref.MTR/2017/000830)supported by the National Natural Science Foundation of China(Ref.11961050)the Guangxi Natural Sciences Foundation(Ref.2021GXNSFAA220043).
文摘Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.In this paper,we investigate the Wiener index and hyper-Wiener index of G(R)and explicitly determine their values.
文摘This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, modified cutwidth, and bandwidth sum(linear arrangement).
基金supported by the National Natural Science Foundation of China under Grant No 60473090the National"11th Five-Year-Supporting-Plan"of China under Grant No 2006BAH02A0407
文摘The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless networks.Investigation of some properties of independent set(IS)in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms.Several constant factor approximation algorithms are presented for the CDS problem in UDGs.Simulation results show that the proposed algorithms perform better than some known ones.
文摘微表情检测旨在视频中定位幅度微弱、时间短暂的表情区间。其难点在于有效提取面部区域间的动态关联特征和多尺度时序特征,进而精准捕捉面部各区域微小动作之间的关联。针对这些问题,提出了一种融合自适应图注意力和多尺度可变空洞卷积的微表情检测网络(AG-DDNet)。通过引入参数可学习矩阵来实现键值对的特征变换,通过计算面部区域特征向量间的相似度得到动态邻接矩阵,并结合图注意力机制计算区域间权重系数,实现特征的动态融合;采用了多尺度可变空洞卷积模块,通过自适应池化与卷积组合的预测器生成动态感受野,从而实现多尺度的特征提取;引入基于Fisher信息矩阵的自然梯度优化机制,通过Fisher Adam优化器有效捕捉参数空间的几何结构信息,实现学习率的精确自适应调整,从而显著增强了模型对微表情和宏表情的协同检测能力。在微表情检测任务中,该算法与同类代表性算法相比,在CAS(ME)2数据集和SAMM Long Videos数据集上的性能分别提升了54.20%和20.11%。与最新算法相比,两个数据集上的提升幅度分别为38.43%和6.81%,有效证明了该方法在长视频微表情检测任务上的优越性能。
基金Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia for funding this research work through the project number RI-44-0028.
文摘The sustainability of the Internet of Things(IoT)involves various issues,such as poor connectivity,scalability problems,interoperability issues,and energy inefficiency.Although the Sixth Generation of mobile networks(6G)allows for Ultra-Reliable Low-Latency Communication(URLLC),enhanced Mobile Broadband(eMBB),and massive Machine-Type Communications(mMTC)services,it faces deployment challenges such as the short range of sub-THz and THz frequency bands,low capability to penetrate obstacles,and very high path loss.This paper presents a network architecture to enhance the connectivity of wireless IoT mesh networks that employ both 6G and Wi-Fi technologies.In this architecture,local communications are carried through the mesh network,which uses a virtual backbone to relay packets to local nodes,while remote communications are carried through the 6G network.The virtual backbone is created using a heuristic distributed ConnectedDominating Set(CDS)algorithm.In this algorithm,each node uses information collected from its one-and two-hop neighbors to determine its role and find the set of expansion nodes that are used to select the next CDS nodes.The proposed algorithm has O(n)message and O(K)time complexities,where n is the number of nodes in the network,and K is the depth of the cluster.The study proved that the approximation ratio of the algorithmhas an upper bound of 2.06748(3.4306MCDS+4.8185).Performance evaluations compared the size of the CDS against the theoretical limit and recent CDS clustering algorithms.Results indicate that the proposed algorithm has the smallest average slope for the size of the CDS as the number of nodes increases.
基金Supported by the National Natural Science Foundation of China(Grant No.11771176)。
文摘In this paper, the automorphism group is completely determined, of the unitary Cayley graph, the unit graph and the total graph, over the ring of Gaussian integers modulo a prime power.
基金Supported by the National Natural Science Foundation of China(Grant No.11971474)the Natural Science Foundation of Shandong Province(Grant No.ZR2019BA016)。
文摘Let T be the subgroup of the multiplicative group C^(×)consisting of all complex numbers z with|z|=1.A T-gain graph is a tripleΦ=(G,T,φ)(or short for(G,φ))consisting of a simple graph G=(V,E),as the underlying graph of(G,Φ),the circle group T and a gain functionΦ:→E→T such that φ(vivj)=φ(vjvi) for any adjacent vertices vi and vj.Let i+(G,φ)(resp.,i+(G))be the positive inertia index of(G,φ)(resp.,G).In this paper,we prove that-c(G)≤i+(G,φ)-i+(G)≤c(G),where c(G)is the cyclomatic number of G,and characterize all the corresponding extremal graphs.
