• Kyungpook Mathematical Journal
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• v.19 no.1
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• pp.127-134
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• 1979

A (0,1) matrix is acyclic if it does not have a permutation matrix of order 2 as a submatrix. A bipartite tournament is acyclic if and only if its adjacency matrix is acyclic. The concepts of (maximal) order of cyclicity of a matrix and a bipartite tournament are introduced and studied.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.95-99
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• 2008

It is known that each eigenvalue of a real symmetric, irreducible, tridiagonal matrix has multiplicity 1. The graph of such a matrix is a path. In this paper, we extend the result by classifying those trees for which each of the associated acyclic matrices has distinct eigenvalues whenever the diagonal entries are distinct.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.285-290
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• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• ETRI Journal
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• v.39 no.4
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• pp.592-604
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• 2017

Intrusion detection is very important for network situation awareness. While a few methods have been proposed to detect network intrusion, they cannot directly and effectively utilize semi-quantitative information consisting of expert knowledge and quantitative data. Hence, this paper proposes a new detection model based on a directed acyclic graph (DAG) and a belief rule base (BRB). In the proposed model, called DAG-BRB, the DAG is employed to construct a multi-layered BRB model that can avoid explosion of combinations of rule number because of a large number of types of intrusion. To obtain the optimal parameters of the DAG-BRB model, an improved constraint covariance matrix adaption evolution strategy (CMA-ES) is developed that can effectively solve the constraint problem in the BRB. A case study was used to test the efficiency of the proposed DAG-BRB. The results showed that compared with other detection models, the DAG-BRB model has a higher detection rate and can be used in real networks.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.135-142
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• 2011

Unlike using the sequence-based representation for a chromosome in previous genetic algorithms for Bayesian structure learning, we proposed a matrix representation-based genetic algorithm. Since a good chromosome representation helps us to develop efficient genetic operators that maintain a functional link between parents and their offspring, we represent a chromosome as a matrix that is a general and intuitive data structure for a directed acyclic graph(DAG), Bayesian network structure. This matrix-based genetic algorithm enables us to develop genetic operators more efficient for structuring Bayesian network: a probability matrix and a transpose-based mutation operator to inherit a structure with the correct edge direction and enhance the diversity of the offspring. To show the outstanding performance of the proposed method, we analyzed the performance between two well-known genetic algorithms and the proposed method using two Bayesian network scoring measures.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.5
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• pp.681-691
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• 1986

To represent the relations of the data dependency and resource conflict among micro-operations(MOP's) in the compaction process of microprograms, we propose a DDM (data dependent matrix) representation method instead of the DAG (conventional directed acyclic graph). Also, we propose a global compaction algorithm of microprograms to prevent a kind of block copying by cutting the trace at a junction block. The DDM method and compaction algoristhm have been applied to the Lah's example. The results shows that the proposed algorithm is more efficient than the conventional algorithms in reducing in reducing the total execution time and control memory space.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.