The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlat...The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks.展开更多
In this paper we prove that the generalized permutation graph G（n, k） is upper embeddable if it has at most two odd subcycles, and that the maximum genus of G（n, k） is more than 「β（G（n,k））/3」 in most cases.
Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is ...Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is obtained the Hausdorff dimension and measure of this construction object for some cases.展开更多
A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χ...A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.展开更多
Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.
The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some gr...The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.展开更多
As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,...As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.展开更多
Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical applicat...Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.展开更多
基金This paper is partially supported by the British Heart Foundation Accelerator Award,UK(AA\18\3\34220)Royal Society International Exchanges Cost Share Award,UK(RP202G0230)+9 种基金Hope Foundation for Cancer Research,UK(RM60G0680)Medical Research Council Confidence in Concept Award,UK(MC_PC_17171)Sino-UK Industrial Fund,UK(RP202G0289)Global Challenges Research Fund(GCRF),UK(P202PF11)LIAS Pioneering Partnerships Award,UK(P202ED10)Data Science Enhancement Fund,UK(P202RE237)Fight for Sight,UK(24NN201)Sino-UK Education Fund,UK(OP202006)Biotechnology and Biological Sciences Research Council,UK(RM32G0178B8)LIAS Seed Corn,UK(P202RE969).
文摘The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks.
基金The NSF (10671073) of Chinathe Scientific Fund (03080045) of the Gathered Talents by Nantong UniversityNSF (07KJB110090) of Jiangsu University.
文摘In this paper we prove that the generalized permutation graph G（n, k） is upper embeddable if it has at most two odd subcycles, and that the maximum genus of G（n, k） is more than 「β（G（n,k））/3」 in most cases.
文摘Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is obtained the Hausdorff dimension and measure of this construction object for some cases.
文摘A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.
文摘Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.
文摘The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.
基金Shanxi Scholarship Council of China(No.2012-070)Foundation of North University of China(No.2013-12-1)
文摘As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.
基金support of the National Natural Science Foundation of China (Grant No. 41130751)China Scholarship Council, Research Program for Western China Communication (Grant No. 2011ZB04)China Central University Funding
文摘Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.
