Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is inc...Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching.展开更多
Text Summarization models facilitate biomedical clinicians and researchers in acquiring informative data from enormous domain-specific literature within less time and effort.Evaluating and selecting the most informati...Text Summarization models facilitate biomedical clinicians and researchers in acquiring informative data from enormous domain-specific literature within less time and effort.Evaluating and selecting the most informative sentences from biomedical articles is always challenging.This study aims to develop a dual-mode biomedical text summarization model to achieve enhanced coverage and information.The research also includes checking the fitment of appropriate graph ranking techniques for improved performance of the summarization model.The input biomedical text is mapped as a graph where meaningful sentences are evaluated as the central node and the critical associations between them.The proposed framework utilizes the top k similarity technique in a combination of UMLS and a sampled probability-based clustering method which aids in unearthing relevant meanings of the biomedical domain-specific word vectors and finding the best possible associations between crucial sentences.The quality of the framework is assessed via different parameters like information retention,coverage,readability,cohesion,and ROUGE scores in clustering and non-clustering modes.The significant benefits of the suggested technique are capturing crucial biomedical information with increased coverage and reasonable memory consumption.The configurable settings of combined parameters reduce execution time,enhance memory utilization,and extract relevant information outperforming other biomedical baseline models.An improvement of 17%is achieved when the proposed model is checked against similar biomedical text summarizers.展开更多
树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)...树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.展开更多
Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are...Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.展开更多
光谱聚类(spectral clustering,SC)由于在无监督学习中的有效性而受到越来越多的关注。然而其计算复杂度高,不适用于处理大规模数据。近年来提出了许多基于锚点图方法来加速大规模光谱聚类,然而这些方法选取的锚点通常不能很好地体现原...光谱聚类(spectral clustering,SC)由于在无监督学习中的有效性而受到越来越多的关注。然而其计算复杂度高,不适用于处理大规模数据。近年来提出了许多基于锚点图方法来加速大规模光谱聚类,然而这些方法选取的锚点通常不能很好地体现原始数据的信息,从而导致聚类性能下降。为克服这些缺陷,提出了一种二分k-means锚点提取的快速谱聚类算法(fast spectral clustering algorithm based on anchor point extraction with bisecting kmeans,FCAPBK)。该方法利用二分k-means从原始数据中选取一些具有代表性的锚点,构建基于锚点的多层无核相似图;然后通过锚点与样本间的相似关系构造层次二部图。最后在5个基准数据集上分别进行实验验证,结果表明FCAPBK方法能够在较短的时间内获得良好的聚类性能。展开更多
文摘Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching.
文摘Text Summarization models facilitate biomedical clinicians and researchers in acquiring informative data from enormous domain-specific literature within less time and effort.Evaluating and selecting the most informative sentences from biomedical articles is always challenging.This study aims to develop a dual-mode biomedical text summarization model to achieve enhanced coverage and information.The research also includes checking the fitment of appropriate graph ranking techniques for improved performance of the summarization model.The input biomedical text is mapped as a graph where meaningful sentences are evaluated as the central node and the critical associations between them.The proposed framework utilizes the top k similarity technique in a combination of UMLS and a sampled probability-based clustering method which aids in unearthing relevant meanings of the biomedical domain-specific word vectors and finding the best possible associations between crucial sentences.The quality of the framework is assessed via different parameters like information retention,coverage,readability,cohesion,and ROUGE scores in clustering and non-clustering modes.The significant benefits of the suggested technique are capturing crucial biomedical information with increased coverage and reasonable memory consumption.The configurable settings of combined parameters reduce execution time,enhance memory utilization,and extract relevant information outperforming other biomedical baseline models.An improvement of 17%is achieved when the proposed model is checked against similar biomedical text summarizers.
文摘树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.
基金The National Natural Science Foundation of China(No.10971025)
文摘Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.
文摘光谱聚类(spectral clustering,SC)由于在无监督学习中的有效性而受到越来越多的关注。然而其计算复杂度高,不适用于处理大规模数据。近年来提出了许多基于锚点图方法来加速大规模光谱聚类,然而这些方法选取的锚点通常不能很好地体现原始数据的信息,从而导致聚类性能下降。为克服这些缺陷,提出了一种二分k-means锚点提取的快速谱聚类算法(fast spectral clustering algorithm based on anchor point extraction with bisecting kmeans,FCAPBK)。该方法利用二分k-means从原始数据中选取一些具有代表性的锚点,构建基于锚点的多层无核相似图;然后通过锚点与样本间的相似关系构造层次二部图。最后在5个基准数据集上分别进行实验验证,结果表明FCAPBK方法能够在较短的时间内获得良好的聚类性能。
