Scene graph prediction has emerged as a critical task in computer vision,focusing on transforming complex visual scenes into structured representations by identifying objects,their attributes,and the relationships amo...Scene graph prediction has emerged as a critical task in computer vision,focusing on transforming complex visual scenes into structured representations by identifying objects,their attributes,and the relationships among them.Extending this to 3D semantic scene graph(3DSSG)prediction introduces an additional layer of complexity because it requires the processing of point-cloud data to accurately capture the spatial and volumetric characteristics of a scene.A significant challenge in 3DSSG is the long-tailed distribution of object and relationship labels,causing certain classes to be severely underrepresented and suboptimal performance in these rare categories.To address this,we proposed a fusion prototypical network(FPN),which combines the strengths of conventional neural networks for 3DSSG with a Prototypical Network.The former are known for their ability to handle complex scene graph predictions while the latter excels in few-shot learning scenarios.By leveraging this fusion,our approach enhances the overall prediction accuracy and substantially improves the handling of underrepresented labels.Through extensive experiments using the 3DSSG dataset,we demonstrated that the FPN achieves state-of-the-art performance in 3D scene graph prediction as a single model and effectively mitigates the impact of the long-tailed distribution,providing a more balanced and comprehensive understanding of complex 3D environments.展开更多
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert...A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.展开更多
Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph...Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.展开更多
It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of ev...It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.展开更多
In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and...In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and inherently sparse.Therefore,it is very difficult to extract long-range contexts and effectively aggregate local features for semantic segmentation in 3D point cloud space.Most current methods either focus on local feature aggregation or long-range context dependency,but fail to directly establish a global-local feature extractor to complete the point cloud semantic segmentation tasks.In this paper,we propose a Transformer-based stratified graph convolutional network(SGT-Net),which enlarges the effective receptive field and builds direct long-range dependency.Specifically,we first propose a novel dense-sparse sampling strategy that provides dense local vertices and sparse long-distance vertices for subsequent graph convolutional network(GCN).Secondly,we propose a multi-key self-attention mechanism based on the Transformer to further weight augmentation for crucial neighboring relationships and enlarge the effective receptive field.In addition,to further improve the efficiency of the network,we propose a similarity measurement module to determine whether the neighborhood near the center point is effective.We demonstrate the validity and superiority of our method on the S3DIS and ShapeNet datasets.Through ablation experiments and segmentation visualization,we verify that the SGT model can improve the performance of the point cloud semantic segmentation.展开更多
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 induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪··...The induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪···∪V(Mk)covers V(G).This paper shows that,if G is a 3-regular claw-free graph,then imc(G)∈{2,3}.展开更多
The increasing frequency of offshore engineering activities,particularly the expansion of offshore oil transport and the rise in the number of oil platforms,has greatly increased the potential risk of marine oil spill...The increasing frequency of offshore engineering activities,particularly the expansion of offshore oil transport and the rise in the number of oil platforms,has greatly increased the potential risk of marine oil spill incidents.Historically,several large oil spills have had long-term adverse effects on marine ecosystems and economic development,highlighting the importance of accurate-ly delineating and monitoring oil spill areas.In this study,graph neural network technology is introduced to implement semantic seg-mentation of SAR images,and two graph neural network models based on Graph-FCN and Graph-DeepLabV3+with the introduction of an attention mechanism are constructed and evaluated to improve the accuracy and efficiency of oil spill detection.By com-paring the Swin-Unet model,the Graph-DeepLabV3+model performs better in complex scenarios,especially in edge detail recognition.This not only provides strong technical support for marine oil spill monitoring but also provides an effective solution to deal with the potential risks brought by the increase of marine engineering activities,which is of great practical significance as it helps to safeguard the health and sustainable development of marine ecosystems and reduce the economic losses.展开更多
Most of local feature descriptors assume that the scene is planar. In the real scene, the captured images come from the 3-D world. 3-D corner as a novel invariant feature is important for the image matching and the ob...Most of local feature descriptors assume that the scene is planar. In the real scene, the captured images come from the 3-D world. 3-D corner as a novel invariant feature is important for the image matching and the object detection, while automatically discriminating 3-D corners from ordinary corners is difficult. A novel method for 3-D corner detection is proposed based on the image graph grammar, and it can detect the 3-D features of corners to some extent. Experimental results show that the method is valid and the 3-D corner is useful for image matching.展开更多
Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the ...Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.展开更多
Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （o...Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （or simply ai） = q ＋ r ＋ dui^＋ - dui^-, bvj （or simply b j） = p ＋ r ＋ d^＋vj - d^-vj and cwk （or simply ck） =p ＋ q ＋ dwk^＋ -dwk^- as the scores of ui in U,vj in V and wk in W respectively. The set A of distinct scores of the vertices of D（U, V, W） is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai（2 ≤ i ≤ n - 1） are even positive integers and an is any positive integer, then for n 〉 3, there exists an oriented 3-partite graph with the score set A ={a1,Σ2i=1 ai,…,Σni=1 ai}, except when A = {0, 2, 3}. Some more results for score sets in oriented 3-partite graphs are obtained.展开更多
An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u...An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.展开更多
Let G be a simple undirected graph.For any real numberα∈[0,1],Nikiforov defined the A_(α)-matrix of G as A_(α)(G)=αD(G)+(1-α)A(G)in 2017,where A(G)and D(G)are the adjacency matrix and the degree diagonal matrix ...Let G be a simple undirected graph.For any real numberα∈[0,1],Nikiforov defined the A_(α)-matrix of G as A_(α)(G)=αD(G)+(1-α)A(G)in 2017,where A(G)and D(G)are the adjacency matrix and the degree diagonal matrix of G,respectively.In this paper,we obtain a lower bound on the A_(α)-spectral radius of a C_(3)-free graph forα∈[0,1)and a sharp upper bound on the Aα-spectral radius of a C_(3)-free k-cycle graph forα∈[1/2,1).展开更多
For integers k 0, r 0, a（k, r）-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} diferent colors. The r-hued chromatic nu...For integers k 0, r 0, a（k, r）-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} diferent colors. The r-hued chromatic number, denoted by χr（G）, is the smallest integer k for which a graph G has a（k, r）-coloring. Define a graph G is r-normal, if χr（G） = χ（G）. In this paper, we present two sufcient conditions for a graph to be 3-normal, and the best upper bound of 3-hued chromatic number of a certain families of graphs.展开更多
Cerenkov Luminescence Tomography(CLT)is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes.However,due to severe ill-posed inverse problem,obtaining accur...Cerenkov Luminescence Tomography(CLT)is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes.However,due to severe ill-posed inverse problem,obtaining accurate reconstruction results is still a challenge for traditional model-based methods.The recently emerged deep learning-based methods can directly learn the mapping relation between the surface photon intensity and the distribution of the radioactive source,which effectively improves the performance of CLT reconstruction.However,the previously proposed deep learning-based methods cannot work well when the order of input is disarranged.In this paper,a novel 3D graph convolution-based residual network,GCR-Net,is proposed,which can obtain a robust and accurate reconstruction result from the photon intensity of the surface.Additionally,it is proved that the network is insensitive to the order of input.The performance of this method was evaluated with numerical simulations and in vivo experiments.The results demonstrated that compared with the existing methods,the proposed method can achieve efficient and accurate reconstruction in localization and shape recovery by utilizing threedimensional information.展开更多
Background In this study,we propose a novel 3D scene graph prediction approach for scene understanding from point clouds.Methods It can automatically organize the entities of a scene in a graph,where objects are nodes...Background In this study,we propose a novel 3D scene graph prediction approach for scene understanding from point clouds.Methods It can automatically organize the entities of a scene in a graph,where objects are nodes and their relationships are modeled as edges.More specifically,we employ the DGCNN to capture the features of objects and their relationships in the scene.A Graph Attention Network(GAT)is introduced to exploit latent features obtained from the initial estimation to further refine the object arrangement in the graph structure.A one loss function modified from cross entropy with a variable weight is proposed to solve the multi-category problem in the prediction of object and predicate.Results Experiments reveal that the proposed approach performs favorably against the state-of-the-art methods in terms of predicate classification and relationship prediction and achieves comparable performance on object classification prediction.Conclusions The 3D scene graph prediction approach can form an abstract description of the scene space from point clouds.展开更多
基金supported by the Glocal University 30 Project Fund of Gyeongsang National University in 2025.
文摘Scene graph prediction has emerged as a critical task in computer vision,focusing on transforming complex visual scenes into structured representations by identifying objects,their attributes,and the relationships among them.Extending this to 3D semantic scene graph(3DSSG)prediction introduces an additional layer of complexity because it requires the processing of point-cloud data to accurately capture the spatial and volumetric characteristics of a scene.A significant challenge in 3DSSG is the long-tailed distribution of object and relationship labels,causing certain classes to be severely underrepresented and suboptimal performance in these rare categories.To address this,we proposed a fusion prototypical network(FPN),which combines the strengths of conventional neural networks for 3DSSG with a Prototypical Network.The former are known for their ability to handle complex scene graph predictions while the latter excels in few-shot learning scenarios.By leveraging this fusion,our approach enhances the overall prediction accuracy and substantially improves the handling of underrepresented labels.Through extensive experiments using the 3DSSG dataset,we demonstrated that the FPN achieves state-of-the-art performance in 3D scene graph prediction as a single model and effectively mitigates the impact of the long-tailed distribution,providing a more balanced and comprehensive understanding of complex 3D environments.
文摘A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.
文摘Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.
基金Supported by National Natural Science Foundation of China(Grant No.12071442)the Fundamental Research Funds for the Central Universities under(Grant No.020314380035)。
文摘It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.U20A20197,62306187the Foundation of Ministry of Industry and Information Technology TC220H05X-04.
文摘In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and inherently sparse.Therefore,it is very difficult to extract long-range contexts and effectively aggregate local features for semantic segmentation in 3D point cloud space.Most current methods either focus on local feature aggregation or long-range context dependency,but fail to directly establish a global-local feature extractor to complete the point cloud semantic segmentation tasks.In this paper,we propose a Transformer-based stratified graph convolutional network(SGT-Net),which enlarges the effective receptive field and builds direct long-range dependency.Specifically,we first propose a novel dense-sparse sampling strategy that provides dense local vertices and sparse long-distance vertices for subsequent graph convolutional network(GCN).Secondly,we propose a multi-key self-attention mechanism based on the Transformer to further weight augmentation for crucial neighboring relationships and enlarge the effective receptive field.In addition,to further improve the efficiency of the network,we propose a similarity measurement module to determine whether the neighborhood near the center point is effective.We demonstrate the validity and superiority of our method on the S3DIS and ShapeNet datasets.Through ablation experiments and segmentation visualization,we verify that the SGT model can improve the performance of the point cloud semantic segmentation.
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Supported by the National Natural Science Foundation of China（10771179）
文摘The induced matching cover number of a graph G without isolated vertices, denoted by imc(G),is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V(M1)∪V(M2)∪···∪V(Mk)covers V(G).This paper shows that,if G is a 3-regular claw-free graph,then imc(G)∈{2,3}.
基金supported by the Natural Science Foun-dation of Shandong Province,China(No.ZR2024QF057)the Natural Science Foundation of Jiangsu Province,China(No.BK20240937)+1 种基金the Natural Science Foundation of China(No.42276215)the China University of Mining and Technology(CUMT)Open Sharing Fund for Large-Scale Instruments and Equipment(No.DYGX-2024-86).
文摘The increasing frequency of offshore engineering activities,particularly the expansion of offshore oil transport and the rise in the number of oil platforms,has greatly increased the potential risk of marine oil spill incidents.Historically,several large oil spills have had long-term adverse effects on marine ecosystems and economic development,highlighting the importance of accurate-ly delineating and monitoring oil spill areas.In this study,graph neural network technology is introduced to implement semantic seg-mentation of SAR images,and two graph neural network models based on Graph-FCN and Graph-DeepLabV3+with the introduction of an attention mechanism are constructed and evaluated to improve the accuracy and efficiency of oil spill detection.By com-paring the Swin-Unet model,the Graph-DeepLabV3+model performs better in complex scenarios,especially in edge detail recognition.This not only provides strong technical support for marine oil spill monitoring but also provides an effective solution to deal with the potential risks brought by the increase of marine engineering activities,which is of great practical significance as it helps to safeguard the health and sustainable development of marine ecosystems and reduce the economic losses.
文摘Most of local feature descriptors assume that the scene is planar. In the real scene, the captured images come from the 3-D world. 3-D corner as a novel invariant feature is important for the image matching and the object detection, while automatically discriminating 3-D corners from ordinary corners is difficult. A novel method for 3-D corner detection is proposed based on the image graph grammar, and it can detect the 3-D features of corners to some extent. Experimental results show that the method is valid and the 3-D corner is useful for image matching.
基金Supported by National Natural Science Foundation of China(Grant Nos.51275438,51405421)Hebei Provincial Natural Science Foundation of China(Grant No.E2015203101)
文摘Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.
文摘Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （or simply ai） = q ＋ r ＋ dui^＋ - dui^-, bvj （or simply b j） = p ＋ r ＋ d^＋vj - d^-vj and cwk （or simply ck） =p ＋ q ＋ dwk^＋ -dwk^- as the scores of ui in U,vj in V and wk in W respectively. The set A of distinct scores of the vertices of D（U, V, W） is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai（2 ≤ i ≤ n - 1） are even positive integers and an is any positive integer, then for n 〉 3, there exists an oriented 3-partite graph with the score set A ={a1,Σ2i=1 ai,…,Σni=1 ai}, except when A = {0, 2, 3}. Some more results for score sets in oriented 3-partite graphs are obtained.
基金The NSF (60673048) of China the NSF (KJ2009B002,KJ2009B237Z) of Education Ministry of Anhui Province.
文摘An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071411,12171222)。
文摘Let G be a simple undirected graph.For any real numberα∈[0,1],Nikiforov defined the A_(α)-matrix of G as A_(α)(G)=αD(G)+(1-α)A(G)in 2017,where A(G)and D(G)are the adjacency matrix and the degree diagonal matrix of G,respectively.In this paper,we obtain a lower bound on the A_(α)-spectral radius of a C_(3)-free graph forα∈[0,1)and a sharp upper bound on the Aα-spectral radius of a C_(3)-free k-cycle graph forα∈[1/2,1).
基金Supported by the Project of Shandong Province Higher Educational Science and Technology Program (Grant No.J10LA11)the Natural Science Foundation of Shandong Province (Grant No.ZR2010AQ003)
文摘For integers k 0, r 0, a（k, r）-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} diferent colors. The r-hued chromatic number, denoted by χr（G）, is the smallest integer k for which a graph G has a（k, r）-coloring. Define a graph G is r-normal, if χr（G） = χ（G）. In this paper, we present two sufcient conditions for a graph to be 3-normal, and the best upper bound of 3-hued chromatic number of a certain families of graphs.
基金National Key Research and Development Program of China (2019YFC1521102)National Natural Science Foundation of China (61701403,61806164,62101439,61906154)+4 种基金China Postdoctoral Science Foundation (2018M643719)Natural Science Foundation of Shaanxi Province (2020JQ-601)Young Talent Support Program of the Shaanxi Association for Science and Technology (20190107)Key Research and Development Program of Shaanxi Province (2019GY-215,2021ZDLSF06-04)Major research and development project of Qinghai (2020-SF-143).
文摘Cerenkov Luminescence Tomography(CLT)is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes.However,due to severe ill-posed inverse problem,obtaining accurate reconstruction results is still a challenge for traditional model-based methods.The recently emerged deep learning-based methods can directly learn the mapping relation between the surface photon intensity and the distribution of the radioactive source,which effectively improves the performance of CLT reconstruction.However,the previously proposed deep learning-based methods cannot work well when the order of input is disarranged.In this paper,a novel 3D graph convolution-based residual network,GCR-Net,is proposed,which can obtain a robust and accurate reconstruction result from the photon intensity of the surface.Additionally,it is proved that the network is insensitive to the order of input.The performance of this method was evaluated with numerical simulations and in vivo experiments.The results demonstrated that compared with the existing methods,the proposed method can achieve efficient and accurate reconstruction in localization and shape recovery by utilizing threedimensional information.
基金Supported by National Natural Science Foundation of China(61872024)National Key R&D Program of China under Grant(2018YFB2100603).
文摘Background In this study,we propose a novel 3D scene graph prediction approach for scene understanding from point clouds.Methods It can automatically organize the entities of a scene in a graph,where objects are nodes and their relationships are modeled as edges.More specifically,we employ the DGCNN to capture the features of objects and their relationships in the scene.A Graph Attention Network(GAT)is introduced to exploit latent features obtained from the initial estimation to further refine the object arrangement in the graph structure.A one loss function modified from cross entropy with a variable weight is proposed to solve the multi-category problem in the prediction of object and predicate.Results Experiments reveal that the proposed approach performs favorably against the state-of-the-art methods in terms of predicate classification and relationship prediction and achieves comparable performance on object classification prediction.Conclusions The 3D scene graph prediction approach can form an abstract description of the scene space from point clouds.
