Let Un be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),...,T_(g))Un be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in the anticlockwise direction)by identifying vi with the root of a...Let Un be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),...,T_(g))Un be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in the anticlockwise direction)by identifying vi with the root of a rooted tree Ti of order ni for each i=1,2,...,g,where ni≥1 and∑^(g)_(i=1)n_(i)=n.Let S(n_(1),n_(2),...,n_(g))be obtained from C(T_(1),T_(2),..,T_(g))by replacing each Ti by a rooted star Sni with the center as its root.Let U(n_(1),n_(2),...,ng)be the set of unicyclic graphs which differ from the unicyclic graph S(n_(1),n_(2),...,n_(g))only up to a permutation of ni's.In this paper,the graph with the minimal least signless Laplacian eigenvalue(respectively,the graph with maximum signless Laplacian spread)in U(n_(1),n_(2),...,n_(g))is determined.展开更多
Most prevailing attention mechanism modules in contemporary research are convolutionbased modules,and while these modules contribute to enhancing the accuracy of deep learning networks in visual tasks,they concurrentl...Most prevailing attention mechanism modules in contemporary research are convolutionbased modules,and while these modules contribute to enhancing the accuracy of deep learning networks in visual tasks,they concurrently augment the overall model complexity.To address the problem,this paper proposes a plug-and-play algorithm that does not increase the complexity of the model,Laplacian attention(LA).The LA algorithm first calculates the similarity distance between feature points in the feature space and feature channel and constructs the residual Laplacian matrix between feature points through the similarity distance and Gaussian kernel.This construction serves to segregate non-similar feature points while aggregating those with similarities.Ultimately,the LA algorithm allocates the outputs of the feature channel and the feature space adaptively to derive the final LA outputs.Crucially,the LA algorithm is confined to the forward computation process and does not involve backpropagation or any parameter learning.The LA algorithm undergoes comprehensive experimentation on three distinct datasets—namely Cifar-10,miniImageNet,and Pascal VOC 2012.The experimental results demonstrate that,compared with the advanced attention mechanism modules in recent years,such as SENet,CBAM,ECANet,coordinate attention,and triplet attention,the LA algorithm exhibits superior performance across image classification,object detection and semantic segmentation tasks.展开更多
In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward ...In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward unit normal to the boundary,and are two nonnegative constants.We establish some universal inequalities for eigenvalues of this problem.展开更多
Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,ter...Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.展开更多
基金This research is supported by NSFC(Nos.12171154,12301438)the Chenguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission(No.23CGA37)。
文摘Let Un be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),...,T_(g))Un be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in the anticlockwise direction)by identifying vi with the root of a rooted tree Ti of order ni for each i=1,2,...,g,where ni≥1 and∑^(g)_(i=1)n_(i)=n.Let S(n_(1),n_(2),...,n_(g))be obtained from C(T_(1),T_(2),..,T_(g))by replacing each Ti by a rooted star Sni with the center as its root.Let U(n_(1),n_(2),...,ng)be the set of unicyclic graphs which differ from the unicyclic graph S(n_(1),n_(2),...,n_(g))only up to a permutation of ni's.In this paper,the graph with the minimal least signless Laplacian eigenvalue(respectively,the graph with maximum signless Laplacian spread)in U(n_(1),n_(2),...,n_(g))is determined.
基金National Natural Science Foundation of China,Grant/Award Number:61967012。
文摘Most prevailing attention mechanism modules in contemporary research are convolutionbased modules,and while these modules contribute to enhancing the accuracy of deep learning networks in visual tasks,they concurrently augment the overall model complexity.To address the problem,this paper proposes a plug-and-play algorithm that does not increase the complexity of the model,Laplacian attention(LA).The LA algorithm first calculates the similarity distance between feature points in the feature space and feature channel and constructs the residual Laplacian matrix between feature points through the similarity distance and Gaussian kernel.This construction serves to segregate non-similar feature points while aggregating those with similarities.Ultimately,the LA algorithm allocates the outputs of the feature channel and the feature space adaptively to derive the final LA outputs.Crucially,the LA algorithm is confined to the forward computation process and does not involve backpropagation or any parameter learning.The LA algorithm undergoes comprehensive experimentation on three distinct datasets—namely Cifar-10,miniImageNet,and Pascal VOC 2012.The experimental results demonstrate that,compared with the advanced attention mechanism modules in recent years,such as SENet,CBAM,ECANet,coordinate attention,and triplet attention,the LA algorithm exhibits superior performance across image classification,object detection and semantic segmentation tasks.
基金Supported by National Natural Science Foundation of China(11001130,12272062)Fundamental Research Funds for the Central Universities(30917011335).
文摘In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward unit normal to the boundary,and are two nonnegative constants.We establish some universal inequalities for eigenvalues of this problem.
基金National Natural Science Foundation of China(No.62372100)。
文摘Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.
