This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bije...A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.展开更多
已有的跨句多元关系抽取工作将输入文本表示为集成句内和句间依赖关系的复杂文档图,但图中包含的噪声信息会影响关系抽取的效果。针对这种情况,该文利用Graph state LSTM获得上下文信息,再分别利用词级注意力机制或位置感知的注意力机制...已有的跨句多元关系抽取工作将输入文本表示为集成句内和句间依赖关系的复杂文档图,但图中包含的噪声信息会影响关系抽取的效果。针对这种情况,该文利用Graph state LSTM获得上下文信息,再分别利用词级注意力机制或位置感知的注意力机制,自动聚焦在对关系抽取起到决定性作用的关键词上,降低噪声信息的影响。并且比较了两种注意力机制对使用Graph state LSTM进行关系抽取的影响。通过在一个重要的精确医学数据集上进行实验,验证了该文所提出模型的有效性。展开更多
The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this pape...The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this paper we obtain the circular chromatic numbers of special graphs such as C t k and C t k-v, and give a simple proof of the circular chromatic number of H m,n .展开更多
A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n^b(it is a complete graph), its co...A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n^b(it is a complete graph), its complement by K_n^b. A non increasing sequence π =(d_1,…,d_n) of nonnegative integers is said to be(a,b,n) graphic if it is realizable by an(a,b,n)-graph. We say a simple graphic sequence π=(d_1,…,d_n) is potentially K_4-K_2∪K_2-graphic if it has a a realization containing an K_4-K_2∪K_2 as a subgraph where K_4 is a complete graph on four vertices and K_2∪K_2 is a set of independent edges. In this paper, we find the smallest degree sum such that every n-term graphical sequence contains K_4-K_2∪K_2 as subgraph.展开更多
The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamilt...The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.展开更多
We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be...We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be the hemagglutinin (HA) gene. Based upon the viral ID identifier of the HA gene sequence, the sequences of all of the genes were sorted into two subsets, depending upon whether the nucleotide occupying the position of maximum entropy, position 658 of the HA sequence, was either A or U. It was found that the information entropy (H) distributions of subsets differed significantly from each other, from H distributions of randomly generated subsets and from the H distributions of the complete datasets of each gene. Mutual information (MI) values facilitated identification of nine nucleotide positions, distributed over seven of the influenza genes, at which the nucleotide subsets were disjoint, or almost disjoint. Nucleotide frequencies at these nine positions were used to compute mutual information values that subsequently served as weighting factors for edges in a graph net-work. Seven of the nucleotide positions in the graph network are sites of synonymous mutations. Three of these sites of synonymous mutation are within a single gene, the M1 gene, which occupied the position of greatest graph centrality. It is proposed that these bioinformatic and network graph results may reflect alterations in M1-mediated viral packaging and exteriorization, known to be susceptible to synonymous mutations.展开更多
In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition o...In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.展开更多
This paper addresses the issue of modeling of the hydraulic long transmission line. In its base, such model is nonlinear with distributed parameters. Since general solution in closed-form for such model in time-domain...This paper addresses the issue of modeling of the hydraulic long transmission line. In its base, such model is nonlinear with distributed parameters. Since general solution in closed-form for such model in time-domain is not available, certain simplifications have to be introduced. The pipeline in the paper has been divided to a cascaded network of n segments so that a model with lumped parameters could be reached. For segment modeling, a standard library of bond graphs element has been used. On the basis of models with lumped parameters, the effect of the number of segments, pipeline length and effective bulk modulus on the dynamics of long transmission line have been analyzed.展开更多
The concept of H-decompositions of graphs was first introduced by Erd?s, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given graphs G and H, an H-decompo...The concept of H-decompositions of graphs was first introduced by Erd?s, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let Ф(n,H) be the smallest number Ф, such that, any graph of order n admits an H-decomposition with at most Ф parts. The exact computation of Ф(n,H) for an arbitrary H is still an open problem. Recently, a few papers have been published about this problem. In this survey we will bring together all the results about H-decompositions. We will also introduce two new related problems, namely Weighted H-Decompositions of graphs and Monochromatic H-Decom- positions of graphs.展开更多
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
文摘A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.
文摘已有的跨句多元关系抽取工作将输入文本表示为集成句内和句间依赖关系的复杂文档图,但图中包含的噪声信息会影响关系抽取的效果。针对这种情况,该文利用Graph state LSTM获得上下文信息,再分别利用词级注意力机制或位置感知的注意力机制,自动聚焦在对关系抽取起到决定性作用的关键词上,降低噪声信息的影响。并且比较了两种注意力机制对使用Graph state LSTM进行关系抽取的影响。通过在一个重要的精确医学数据集上进行实验,验证了该文所提出模型的有效性。
文摘The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this paper we obtain the circular chromatic numbers of special graphs such as C t k and C t k-v, and give a simple proof of the circular chromatic number of H m,n .
文摘A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n^b(it is a complete graph), its complement by K_n^b. A non increasing sequence π =(d_1,…,d_n) of nonnegative integers is said to be(a,b,n) graphic if it is realizable by an(a,b,n)-graph. We say a simple graphic sequence π=(d_1,…,d_n) is potentially K_4-K_2∪K_2-graphic if it has a a realization containing an K_4-K_2∪K_2 as a subgraph where K_4 is a complete graph on four vertices and K_2∪K_2 is a set of independent edges. In this paper, we find the smallest degree sum such that every n-term graphical sequence contains K_4-K_2∪K_2 as subgraph.
文摘The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.
文摘We report a bioinformatic analysis of the datasets of sequences of all ten genes from the 2009 H1N1 influenza A pandemic in the state of Wisconsin. The gene with the greatest summed information entropy was found to be the hemagglutinin (HA) gene. Based upon the viral ID identifier of the HA gene sequence, the sequences of all of the genes were sorted into two subsets, depending upon whether the nucleotide occupying the position of maximum entropy, position 658 of the HA sequence, was either A or U. It was found that the information entropy (H) distributions of subsets differed significantly from each other, from H distributions of randomly generated subsets and from the H distributions of the complete datasets of each gene. Mutual information (MI) values facilitated identification of nine nucleotide positions, distributed over seven of the influenza genes, at which the nucleotide subsets were disjoint, or almost disjoint. Nucleotide frequencies at these nine positions were used to compute mutual information values that subsequently served as weighting factors for edges in a graph net-work. Seven of the nucleotide positions in the graph network are sites of synonymous mutations. Three of these sites of synonymous mutation are within a single gene, the M1 gene, which occupied the position of greatest graph centrality. It is proposed that these bioinformatic and network graph results may reflect alterations in M1-mediated viral packaging and exteriorization, known to be susceptible to synonymous mutations.
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 1 1 0 )
文摘In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.
文摘This paper addresses the issue of modeling of the hydraulic long transmission line. In its base, such model is nonlinear with distributed parameters. Since general solution in closed-form for such model in time-domain is not available, certain simplifications have to be introduced. The pipeline in the paper has been divided to a cascaded network of n segments so that a model with lumped parameters could be reached. For segment modeling, a standard library of bond graphs element has been used. On the basis of models with lumped parameters, the effect of the number of segments, pipeline length and effective bulk modulus on the dynamics of long transmission line have been analyzed.
文摘The concept of H-decompositions of graphs was first introduced by Erd?s, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let Ф(n,H) be the smallest number Ф, such that, any graph of order n admits an H-decomposition with at most Ф parts. The exact computation of Ф(n,H) for an arbitrary H is still an open problem. Recently, a few papers have been published about this problem. In this survey we will bring together all the results about H-decompositions. We will also introduce two new related problems, namely Weighted H-Decompositions of graphs and Monochromatic H-Decom- positions of graphs.
