Genes associated with similar diseases are often functionally related.This principle is largely supported by many biological data sources,such as disease phenotype similarities,protein complexes,protein-protein intera...Genes associated with similar diseases are often functionally related.This principle is largely supported by many biological data sources,such as disease phenotype similarities,protein complexes,protein-protein interactions,pathways and gene expression profiles.Integrating multiple types of biological data is an effective method to identify disease genes for many genetic diseases.To capture the gene-disease associations based on biological networks,a kernel-based Markov random field(MRF)method is proposed by combining graph kernels and the MRF method.In the proposed method,three kinds of kernels are employed to describe the overall relationships of vertices in five biological networks,respectively,and a novel weighted MRF method is developed to integrate those data.In addition,an improved Gibbs sampling procedure and a novel parameter estimation method are proposed to generate predictions from the kernel-based MRF method.Numerical experiments are carried out by integrating known gene-disease associations,protein complexes,protein-protein interactions,pathways and gene expression profiles.The proposed kernel-based MRF method is evaluated by the leave-one-out cross validation paradigm,achieving an AUC score of 0.771 when integrating all those biological data in our experiments,which indicates that our proposed method is very promising compared with many existing methods.展开更多
In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of deg...In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of degree m,the initial values,and the exponents in absorption terms,we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time.Our current work extends the results achieved by Lin and Wu(Calc Var Partial Differ Equ,2017,56:Art 102)and Wu(Rev R Acad Cien Serie A Mat,2021,115:Art 133).展开更多
This article is devoted to developing a deep learning method for the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computation...This article is devoted to developing a deep learning method for the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computationally numerical format has been used. In particular, for investigation mathematical models of the dynamical system of cancer cell invasion in inhomogeneous areas of human tissues have been considered. Neural operators were initially proposed to model the differential operator of PDEs. The GKNN mapping features between input data to the PDEs and their solutions have been constructed. The boundary integral method in combination with Green’s functions for a large number of boundary conditions is used. The tools applied in this development are based on the Fourier neural operators (FNOs), graph theory, theory elasticity, and singular integral equations.展开更多
Most news topic detection methods use word-based methods,which easily ignore the relationship among words and have semantic sparsity,resulting in low topic detection accuracy.In addition,the current mainstream probabi...Most news topic detection methods use word-based methods,which easily ignore the relationship among words and have semantic sparsity,resulting in low topic detection accuracy.In addition,the current mainstream probability methods and graph analysis methods for topic detection have high time complexity.For these reasons,we present a news topic detection model on the basis of capsule semantic graph(CSG).The keywords that appear in each text at the same time are modeled as a keyword graph,which is divided into multiple subgraphs through community detection.Each subgraph contains a group of closely related keywords.The graph is used as the vertex of CSG.The semantic relationship among the vertices is obtained by calculating the similarity of the average word vector of each vertex.At the same time,the news text is clustered using the incremental clustering method,where each text uses CSG;that is,the similarity among texts is calculated by the graph kernel.The relationship between vertices and edges is also considered when calculating the similarity.Experimental results on three standard datasets show that CSG can obtain higher precision,recall,and F1 values than several latest methods.Experimental results on large-scale news datasets reveal that the time complexity of CSG is lower than that of probabilistic methods and other graph analysis methods.展开更多
The community stability of coral reefs and fish is the focus of ecological monitoring of coral reefs.Among them,the realization of effective metrics of variations in reef fish communities(i.e.,the combined communities...The community stability of coral reefs and fish is the focus of ecological monitoring of coral reefs.Among them,the realization of effective metrics of variations in reef fish communities(i.e.,the combined communities of coral reefs and fish)is important for analyzing the stability of communities as well as maintaining the ecological balance of coral reefs.Based on coral reef and fish data collected at St.John’s Island from 2004 to 2010,this study proposes a symbiotic graph modeling method to express the biological relationships of reef fish communities,and a Pyramid Match graph kernel method for fusing Attributes(PMA)to quantify community fluctuations to measure interannual variability of communities.The results showed that the community similarity was low in 2006,2007,and 2008.The total coral cover rate in the study area decreased by 32.04% from 2006 to 2007 and increased by 24% in 2008.The total number of fish fell from 3780 in 2006 to 2596 in 2007 and rose to 6249 in 2008.Among them,the proportion of herbivorous fish decreased to 30.84% in 2007.Furthermore,we have combined the Louvain algorithm with the proposed PMA method to effectively identify the regions that should be prioritized for protection.Experiments were conducted on real datasets with good results,demonstrating the potential of the proposed method to assist in the analysis of community stability and identification of priority conservation areas.展开更多
Kernelization algorithms for graph modification problems are important ingredients in parameterized computation theory. In this paper, we survey the kernelization algorithms for four types of graph modification proble...Kernelization algorithms for graph modification problems are important ingredients in parameterized computation theory. In this paper, we survey the kernelization algorithms for four types of graph modification problems, which include vertex deletion problems, edge editing problems, edge deletion problems, and edge completion problems. For each type of problem, we outline typical examples together with recent results, analyze the main techniques, and provide some suggestions for future research in this field.展开更多
Background Brain network describing interconnections between brain regions contains abundant topological information.It is a challenge for the existing statistical methods(e.g.,t test)to investigate the topological di...Background Brain network describing interconnections between brain regions contains abundant topological information.It is a challenge for the existing statistical methods(e.g.,t test)to investigate the topological differences of brain networks.Methods We proposed a kernel based statistic framework for identifying topological differences in brain networks.In our framework,the topological similarities between paired brain networks were measured by graph kernels.Then,graph kernels are embedded into maximum mean discrepancy for calculating kernel based test statistic.Based on this test statistic,we adopted conditional Monte Carlo simulation to compute the statistical significance(i.e.,P value)and statistical power.We recruited 33 patients with Alzheimer’s disease(AD),33 patients with early mild cognitive impairment(EMCI),33 patients with late mild cognitive impairment(LMCI)and 33 normal controls(NC)in our experiment.There are no statistical differences in demographic information between patients and NC.The compared state-of-the-art statistical methods include t test,t squared test,two-sample permutation test and non-normal test.Results We applied the proposed shortest path matched kernel to our framework for investigating the statistical differences of shortest path topological structures in brain networks of AD and NC.We compared our method with the existing state-of-the-art statistical methods in brain network characteristic including clustering coefficient and functional connection among EMCI,LMCI,AD,and NC.The results indicate that our framework can capture the statistically discriminative shortest path topological structures,such as shortest path from right rolandic operculum to right supplementary motor area(P=0.00314,statistical power=0.803).In clustering coefficient and functional connection,our framework outperforms the state-of-the-art statistical methods,such as P=0.0013 and statistical power=0.83 in the analysis of AD and NC.Conclusion Our proposed kernel based statistic framework not only can be used to investigate the topological differences of brain network,but also can be used to investigate the static characteristics(e.g.,clustering coefficient and functional connection)of brain network.展开更多
基金supported by the Natural Sciences and Engineering Research Council of CanadaNational Natural Science Foundation of China(61428209,61232001)
文摘Genes associated with similar diseases are often functionally related.This principle is largely supported by many biological data sources,such as disease phenotype similarities,protein complexes,protein-protein interactions,pathways and gene expression profiles.Integrating multiple types of biological data is an effective method to identify disease genes for many genetic diseases.To capture the gene-disease associations based on biological networks,a kernel-based Markov random field(MRF)method is proposed by combining graph kernels and the MRF method.In the proposed method,three kinds of kernels are employed to describe the overall relationships of vertices in five biological networks,respectively,and a novel weighted MRF method is developed to integrate those data.In addition,an improved Gibbs sampling procedure and a novel parameter estimation method are proposed to generate predictions from the kernel-based MRF method.Numerical experiments are carried out by integrating known gene-disease associations,protein complexes,protein-protein interactions,pathways and gene expression profiles.The proposed kernel-based MRF method is evaluated by the leave-one-out cross validation paradigm,achieving an AUC score of 0.771 when integrating all those biological data in our experiments,which indicates that our proposed method is very promising compared with many existing methods.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(LY21A010016)the National Natural Science Foundation of China(11901550).
文摘In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of degree m,the initial values,and the exponents in absorption terms,we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time.Our current work extends the results achieved by Lin and Wu(Calc Var Partial Differ Equ,2017,56:Art 102)and Wu(Rev R Acad Cien Serie A Mat,2021,115:Art 133).
文摘This article is devoted to developing a deep learning method for the numerical solution of the partial differential equations (PDEs). Graph kernel neural networks (GKNN) approach to embedding graphs into a computationally numerical format has been used. In particular, for investigation mathematical models of the dynamical system of cancer cell invasion in inhomogeneous areas of human tissues have been considered. Neural operators were initially proposed to model the differential operator of PDEs. The GKNN mapping features between input data to the PDEs and their solutions have been constructed. The boundary integral method in combination with Green’s functions for a large number of boundary conditions is used. The tools applied in this development are based on the Fourier neural operators (FNOs), graph theory, theory elasticity, and singular integral equations.
文摘Most news topic detection methods use word-based methods,which easily ignore the relationship among words and have semantic sparsity,resulting in low topic detection accuracy.In addition,the current mainstream probability methods and graph analysis methods for topic detection have high time complexity.For these reasons,we present a news topic detection model on the basis of capsule semantic graph(CSG).The keywords that appear in each text at the same time are modeled as a keyword graph,which is divided into multiple subgraphs through community detection.Each subgraph contains a group of closely related keywords.The graph is used as the vertex of CSG.The semantic relationship among the vertices is obtained by calculating the similarity of the average word vector of each vertex.At the same time,the news text is clustered using the incremental clustering method,where each text uses CSG;that is,the similarity among texts is calculated by the graph kernel.The relationship between vertices and edges is also considered when calculating the similarity.Experimental results on three standard datasets show that CSG can obtain higher precision,recall,and F1 values than several latest methods.Experimental results on large-scale news datasets reveal that the time complexity of CSG is lower than that of probabilistic methods and other graph analysis methods.
基金supported by the National Natural Science Foundation of China[No.42106190]the Science and Technology Commission of Shanghai Municipality Capacity Building Plan for Some Regional Universities and Colleges[No.20050501900].
文摘The community stability of coral reefs and fish is the focus of ecological monitoring of coral reefs.Among them,the realization of effective metrics of variations in reef fish communities(i.e.,the combined communities of coral reefs and fish)is important for analyzing the stability of communities as well as maintaining the ecological balance of coral reefs.Based on coral reef and fish data collected at St.John’s Island from 2004 to 2010,this study proposes a symbiotic graph modeling method to express the biological relationships of reef fish communities,and a Pyramid Match graph kernel method for fusing Attributes(PMA)to quantify community fluctuations to measure interannual variability of communities.The results showed that the community similarity was low in 2006,2007,and 2008.The total coral cover rate in the study area decreased by 32.04% from 2006 to 2007 and increased by 24% in 2008.The total number of fish fell from 3780 in 2006 to 2596 in 2007 and rose to 6249 in 2008.Among them,the proportion of herbivorous fish decreased to 30.84% in 2007.Furthermore,we have combined the Louvain algorithm with the proposed PMA method to effectively identify the regions that should be prioritized for protection.Experiments were conducted on real datasets with good results,demonstrating the potential of the proposed method to assist in the analysis of community stability and identification of priority conservation areas.
基金supported by the National Natural Science Foundation of China (Nos. 61070224, 61232001, and 61173051)the China Postdoctoral Science Foundation (No. 2012M521551)
文摘Kernelization algorithms for graph modification problems are important ingredients in parameterized computation theory. In this paper, we survey the kernelization algorithms for four types of graph modification problems, which include vertex deletion problems, edge editing problems, edge deletion problems, and edge completion problems. For each type of problem, we outline typical examples together with recent results, analyze the main techniques, and provide some suggestions for future research in this field.
基金supported by the National Natural Science Foundation of China(Grant Nos.61876082,61732006,and 61861130366)the National Key R&D Program of China(Grant Nos.2018YFC2001600,2018YFC2001602,and 2018ZX10201002)the Royal Society Academy of Medical Sciences Newton Advanced Fellowship(Grant No.NAF\R1\180371).
文摘Background Brain network describing interconnections between brain regions contains abundant topological information.It is a challenge for the existing statistical methods(e.g.,t test)to investigate the topological differences of brain networks.Methods We proposed a kernel based statistic framework for identifying topological differences in brain networks.In our framework,the topological similarities between paired brain networks were measured by graph kernels.Then,graph kernels are embedded into maximum mean discrepancy for calculating kernel based test statistic.Based on this test statistic,we adopted conditional Monte Carlo simulation to compute the statistical significance(i.e.,P value)and statistical power.We recruited 33 patients with Alzheimer’s disease(AD),33 patients with early mild cognitive impairment(EMCI),33 patients with late mild cognitive impairment(LMCI)and 33 normal controls(NC)in our experiment.There are no statistical differences in demographic information between patients and NC.The compared state-of-the-art statistical methods include t test,t squared test,two-sample permutation test and non-normal test.Results We applied the proposed shortest path matched kernel to our framework for investigating the statistical differences of shortest path topological structures in brain networks of AD and NC.We compared our method with the existing state-of-the-art statistical methods in brain network characteristic including clustering coefficient and functional connection among EMCI,LMCI,AD,and NC.The results indicate that our framework can capture the statistically discriminative shortest path topological structures,such as shortest path from right rolandic operculum to right supplementary motor area(P=0.00314,statistical power=0.803).In clustering coefficient and functional connection,our framework outperforms the state-of-the-art statistical methods,such as P=0.0013 and statistical power=0.83 in the analysis of AD and NC.Conclusion Our proposed kernel based statistic framework not only can be used to investigate the topological differences of brain network,but also can be used to investigate the static characteristics(e.g.,clustering coefficient and functional connection)of brain network.
