Previous multi-view 3D human pose estimation methods neither correlate different human joints in each view nor model learnable correlations between the same joints in different views explicitly,meaning that skeleton s...Previous multi-view 3D human pose estimation methods neither correlate different human joints in each view nor model learnable correlations between the same joints in different views explicitly,meaning that skeleton structure information is not utilized and multi-view pose information is not completely fused.Moreover,existing graph convolutional operations do not consider the specificity of different joints and different views of pose information when processing skeleton graphs,making the correlation weights between nodes in the graph and their neighborhood nodes shared.Existing Graph Convolutional Networks(GCNs)cannot extract global and deeplevel skeleton structure information and view correlations efficiently.To solve these problems,pre-estimated multiview 2D poses are designed as a multi-view skeleton graph to fuse skeleton priors and view correlations explicitly to process occlusion problem,with the skeleton-edge and symmetry-edge representing the structure correlations between adjacent joints in each viewof skeleton graph and the view-edge representing the view correlations between the same joints in different views.To make graph convolution operation mine elaborate and sufficient skeleton structure information and view correlations,different correlation weights are assigned to different categories of neighborhood nodes and further assigned to each node in the graph.Based on the graph convolution operation proposed above,a Residual Graph Convolution(RGC)module is designed as the basic module to be combined with the simplified Hourglass architecture to construct the Hourglass-GCN as our 3D pose estimation network.Hourglass-GCNwith a symmetrical and concise architecture processes three scales ofmulti-viewskeleton graphs to extract local-to-global scale and shallow-to-deep level skeleton features efficiently.Experimental results on common large 3D pose dataset Human3.6M and MPI-INF-3DHP show that Hourglass-GCN outperforms some excellent methods in 3D pose estimation accuracy.展开更多
The partition of indeterminacy function of the neutrosophic set into the contradiction part and the ignorance part represent the quadripartitioned single valued neutrosophic set.In this work,the new concept of quadrip...The partition of indeterminacy function of the neutrosophic set into the contradiction part and the ignorance part represent the quadripartitioned single valued neutrosophic set.In this work,the new concept of quadripartitioned bipolar single valued neutrosophic graph is established,and the operations on it are studied.The Cartesian product,cross product,lexicographic product,strong product and composition of quadripartitioned bipolar single valued neutrosophic graph are investigated.The proposed concepts are illustrated with examples.展开更多
The Lanzhou index of a graph G is defined as the sum of the product between <img src="Edit_267e1b98-b5dd-40b4-b5f0-c9e5e012d359.bmp" alt="" /> and square of d<sub>u</sub> over all...The Lanzhou index of a graph G is defined as the sum of the product between <img src="Edit_267e1b98-b5dd-40b4-b5f0-c9e5e012d359.bmp" alt="" /> and square of d<sub>u</sub> over all vertices u of G, where d<sub>u</sub> and <img src="Edit_0cc51468-628a-4a8a-8205-eec1f93624aa.bmp" alt="" /> are respectively the degree of u in G and the degree of u in the complement graph <img src="Edit_2027b773-bcdd-4cbc-b746-bd9b93390798.bmp" alt="" />of G. R(G) is obtained from G by adding a new vertex corresponding to each edge of G, then joining each new vertex to the end vertices of the corresponding edge. Lanzhou index is an important topological index. It is closely related to the forgotten index and first Zagreb index of graphs. In this note, we characterize the bound of Lanzhou index of R(T) of a tree T. And the corresponding extremal graphs are also determined.展开更多
We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions...We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions of symmetric Schr?dinger operator, initially defined on a smooth function, whose support does not contain the branch points of the graph and branch points of the manifold. These results are obtained for graphs with a single vertex, graphs with multiple vertices and graphs with a single vertex and countable set of rays.展开更多
With the rapid progress in data-driven approaches,artificial intelligence,and big data analytics technologies,utilizing electroencephalogram(EEG)signals for emotion analysis in the field of the Internet of Medical Thi...With the rapid progress in data-driven approaches,artificial intelligence,and big data analytics technologies,utilizing electroencephalogram(EEG)signals for emotion analysis in the field of the Internet of Medical Things can effectively assist in the diagnosis of specific diseases.While existing emotion analysis methods focus on the utilization of effective deep models for data-driven and big data analytics technology,they often struggle to extract long-range dependencies and accurately model local relationships within multi-channel EEG signals.In addition,the subjective scores of the subjects may not match the predefined emotional labels.To overcome these limitations,this paper proposes a new data-driven dynamic graph-embedded Transformer network(DGETN)that has emerged in different tasks of graph data mining for emotion analysis of EEG signals in the scene of IoMT.Firstly,we extract the frequency features differential entropy(DE)and use the linear dynamic system(LDS)method to alleviate the redundancy and noise information.Secondly,to effectively explore the long-range information and local modeling ability,a novel feature extraction module is designed by embedding the dynamic graph convolution operations in the Transformer encoder for mining the discriminant features of data.Moreover,the graph convolution operations can effectively exploit the spatial information between different channels.At last,we introduce the minimum category confusion(MCC)loss to alleviate the fuzziness of classification.We take two commonly used EEG sentiment analysis datasets as a study.The DGETN has achieved state-of-the-art accuracies of 99.38%on the SEED dataset,and accuracies of 99.24%and 98.85%for valence and arousal prediction on the DEAP dataset,respectively.展开更多
In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β（u）-div（α（x, Du）＋F（u）） ∈ f in fΩ, where f ∈ L1 （Ω）. A vector field a（.,....In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β（u）-div（α（x, Du）＋F（u）） ∈ f in fΩ, where f ∈ L1 （Ω）. A vector field a（.,.） is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.展开更多
Inexact graph matching algorithms have proved to be useful in many applications,such as character recognition,shape analysis,and image analysis. Inexact graph matching is,however,inherently an NP-hard problem with exp...Inexact graph matching algorithms have proved to be useful in many applications,such as character recognition,shape analysis,and image analysis. Inexact graph matching is,however,inherently an NP-hard problem with exponential computational complexity. Much of the previous research has focused on solving this problem using heuristics or estimations. Unfortunately,many of these techniques do not guarantee that an optimal solution will be found. It is the aim of the proposed algorithm to reduce the complexity of the inexact graph matching process,while still producing an optimal solution for a known application. This is achieved by greatly simplifying each individual matching process,and compensating for lost robustness by producing a hierarchy of matching processes. The creation of each matching process in the hierarchy is driven by an application-specific criterion that operates at the subgraph scale. To our knowledge,this problem has never before been approached in this manner. Results show that the proposed algorithm is faster than two existing methods based on graph edit operations.The proposed algorithm produces accurate results in terms of matching graphs,and shows promise for the application of shape matching. The proposed algorithm can easily be extended to produce a sub-optimal solution if required.展开更多
Following the previous work,we shall study some inverse problems for the Dirac operator on an equilateral star graph.It is proven that the so-called Weyl function uniquely determines the potentials.Furthermore,we pay ...Following the previous work,we shall study some inverse problems for the Dirac operator on an equilateral star graph.It is proven that the so-called Weyl function uniquely determines the potentials.Furthermore,we pay attention to the inverse problem of recovering the potentials from the spectral data,which consists of the eigenvalues and weight matrices,and present a constructive algorithm.The basic tool in this paper is the method of spectral mappings developed by Yurko.展开更多
基金supported in part by the National Natural Science Foundation of China under Grants 61973065,U20A20197,61973063.
文摘Previous multi-view 3D human pose estimation methods neither correlate different human joints in each view nor model learnable correlations between the same joints in different views explicitly,meaning that skeleton structure information is not utilized and multi-view pose information is not completely fused.Moreover,existing graph convolutional operations do not consider the specificity of different joints and different views of pose information when processing skeleton graphs,making the correlation weights between nodes in the graph and their neighborhood nodes shared.Existing Graph Convolutional Networks(GCNs)cannot extract global and deeplevel skeleton structure information and view correlations efficiently.To solve these problems,pre-estimated multiview 2D poses are designed as a multi-view skeleton graph to fuse skeleton priors and view correlations explicitly to process occlusion problem,with the skeleton-edge and symmetry-edge representing the structure correlations between adjacent joints in each viewof skeleton graph and the view-edge representing the view correlations between the same joints in different views.To make graph convolution operation mine elaborate and sufficient skeleton structure information and view correlations,different correlation weights are assigned to different categories of neighborhood nodes and further assigned to each node in the graph.Based on the graph convolution operation proposed above,a Residual Graph Convolution(RGC)module is designed as the basic module to be combined with the simplified Hourglass architecture to construct the Hourglass-GCN as our 3D pose estimation network.Hourglass-GCNwith a symmetrical and concise architecture processes three scales ofmulti-viewskeleton graphs to extract local-to-global scale and shallow-to-deep level skeleton features efficiently.Experimental results on common large 3D pose dataset Human3.6M and MPI-INF-3DHP show that Hourglass-GCN outperforms some excellent methods in 3D pose estimation accuracy.
基金the Taif University Researchers Supporting Project(TURSP-2020/246),Taif University,Taif,Saudi Arabia.
文摘The partition of indeterminacy function of the neutrosophic set into the contradiction part and the ignorance part represent the quadripartitioned single valued neutrosophic set.In this work,the new concept of quadripartitioned bipolar single valued neutrosophic graph is established,and the operations on it are studied.The Cartesian product,cross product,lexicographic product,strong product and composition of quadripartitioned bipolar single valued neutrosophic graph are investigated.The proposed concepts are illustrated with examples.
文摘The Lanzhou index of a graph G is defined as the sum of the product between <img src="Edit_267e1b98-b5dd-40b4-b5f0-c9e5e012d359.bmp" alt="" /> and square of d<sub>u</sub> over all vertices u of G, where d<sub>u</sub> and <img src="Edit_0cc51468-628a-4a8a-8205-eec1f93624aa.bmp" alt="" /> are respectively the degree of u in G and the degree of u in the complement graph <img src="Edit_2027b773-bcdd-4cbc-b746-bd9b93390798.bmp" alt="" />of G. R(G) is obtained from G by adding a new vertex corresponding to each edge of G, then joining each new vertex to the end vertices of the corresponding edge. Lanzhou index is an important topological index. It is closely related to the forgotten index and first Zagreb index of graphs. In this note, we characterize the bound of Lanzhou index of R(T) of a tree T. And the corresponding extremal graphs are also determined.
文摘We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of self-adjoint extensions of symmetric Schr?dinger operator, initially defined on a smooth function, whose support does not contain the branch points of the graph and branch points of the manifold. These results are obtained for graphs with a single vertex, graphs with multiple vertices and graphs with a single vertex and countable set of rays.
文摘With the rapid progress in data-driven approaches,artificial intelligence,and big data analytics technologies,utilizing electroencephalogram(EEG)signals for emotion analysis in the field of the Internet of Medical Things can effectively assist in the diagnosis of specific diseases.While existing emotion analysis methods focus on the utilization of effective deep models for data-driven and big data analytics technology,they often struggle to extract long-range dependencies and accurately model local relationships within multi-channel EEG signals.In addition,the subjective scores of the subjects may not match the predefined emotional labels.To overcome these limitations,this paper proposes a new data-driven dynamic graph-embedded Transformer network(DGETN)that has emerged in different tasks of graph data mining for emotion analysis of EEG signals in the scene of IoMT.Firstly,we extract the frequency features differential entropy(DE)and use the linear dynamic system(LDS)method to alleviate the redundancy and noise information.Secondly,to effectively explore the long-range information and local modeling ability,a novel feature extraction module is designed by embedding the dynamic graph convolution operations in the Transformer encoder for mining the discriminant features of data.Moreover,the graph convolution operations can effectively exploit the spatial information between different channels.At last,we introduce the minimum category confusion(MCC)loss to alleviate the fuzziness of classification.We take two commonly used EEG sentiment analysis datasets as a study.The DGETN has achieved state-of-the-art accuracies of 99.38%on the SEED dataset,and accuracies of 99.24%and 98.85%for valence and arousal prediction on the DEAP dataset,respectively.
文摘In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β（u）-div（α（x, Du）＋F（u）） ∈ f in fΩ, where f ∈ L1 （Ω）. A vector field a（.,.） is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.
文摘Inexact graph matching algorithms have proved to be useful in many applications,such as character recognition,shape analysis,and image analysis. Inexact graph matching is,however,inherently an NP-hard problem with exponential computational complexity. Much of the previous research has focused on solving this problem using heuristics or estimations. Unfortunately,many of these techniques do not guarantee that an optimal solution will be found. It is the aim of the proposed algorithm to reduce the complexity of the inexact graph matching process,while still producing an optimal solution for a known application. This is achieved by greatly simplifying each individual matching process,and compensating for lost robustness by producing a hierarchy of matching processes. The creation of each matching process in the hierarchy is driven by an application-specific criterion that operates at the subgraph scale. To our knowledge,this problem has never before been approached in this manner. Results show that the proposed algorithm is faster than two existing methods based on graph edit operations.The proposed algorithm produces accurate results in terms of matching graphs,and shows promise for the application of shape matching. The proposed algorithm can easily be extended to produce a sub-optimal solution if required.
基金Supported by NSFC(Grant No.11871031)the Natural Science Foundation of the Jiangsu Province of China(Grant No.BK20201303)。
文摘Following the previous work,we shall study some inverse problems for the Dirac operator on an equilateral star graph.It is proven that the so-called Weyl function uniquely determines the potentials.Furthermore,we pay attention to the inverse problem of recovering the potentials from the spectral data,which consists of the eigenvalues and weight matrices,and present a constructive algorithm.The basic tool in this paper is the method of spectral mappings developed by Yurko.
