• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.228-233
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• 2005

The protein side-chain packing problem (SCPP) is known to be NP-complete. Various graph theoretic based side-chain packing algorithms have been proposed. However as the size of the protein becomes larger, the sampling space increases exponentially. Hence, one approach to cope with the time complexity is to decompose the graph of the protein into smaller subgraphs. Some existing approaches decompose the graph into biconnected components at an articulation point (resulting in an at-most 21-residue subgraph) or solve the SCPP by tree decomposition (4-, 5-residue subgraph). In this regard, we had also presented a deterministic based approach called as SPWCQ using the notion of maximum edge weight clique in which we reduce SCPP to a graph and then obtain the maximum edge-weight clique of the obtained graph. This algorithm performs well for a protein of less than 500 residues. However, it fails to produce a feasible solution for larger proteins because of the size of the search space. In this paper, we present a new heuristic approach for the side-chain packing problem based on the maximum edge-weight clique finding algorithm that enables us to compute the side-chain packing of much larger proteins. Our new approach can compute side-chain packing of a protein of 874 residues with an RMSD of 1.423${\AA}$.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.437-453
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• 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ~ on S defined by letting a ~ b if and only if ann_S(a) = ann_S(b), is an equivalence relation. The compressed zero-divisor graph 𝚪_E(S) of S is the undirected graph whose vertices are the equivalence classes induced by ~ on S other than [0]_S and [1]_S, in which two distinct vertices [a]_S and [b]_S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R₀[x] and the near-ring of the power series R₀[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam(𝚪_E(R₀[x])) and diam(𝚪_E(R₀[[x]])). As a corollary, it is shown that for a reduced ring R, diam(𝚪_E(R)) ≤ diam(𝚪_E(R₀[x])) ≤ diam(𝚪_E(R₀[[x]])).

• Steel and Composite Structures
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• v.44 no.2
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• pp.241-254
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• 2022

The cables in a cable-stayed bridge are critical load-carrying parts. The potential damage to cables should be identified early to prevent disasters. In this study, an efficient deep learning model is proposed for the damage identification of cables using both a multi-layer perceptron (MLP) and a graph neural network (GNN). Datasets are first generated using the practical advanced analysis program (PAAP), which is a robust program for modeling and analyzing bridge structures with low computational costs. The model based on the MLP and GNN can capture complex nonlinear correlations between the vibration characteristics in the input data and the cable system damage in the output data. Multiple hidden layers with an activation function are used in the MLP to expand the original input vector of the limited measurement data to obtain a complete output data vector that preserves sufficient information for constructing the graph in the GNN. Using the gated recurrent unit and set2set model, the GNN maps the formed graph feature to the output cable damage through several updating times and provides the damage results to both the classification and regression outputs. The model is fine-tuned with the original input data using Adam optimization for the final objective function. A case study of an actual cable-stayed bridge was considered to evaluate the model performance. The results demonstrate that the proposed model provides high accuracy (over 90%) in classification and satisfactory correlation coefficients (over 0.98) in regression and is a robust approach to obtain effective identification results with a limited quantity of input data.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.155-167
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• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.49-58
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• 2009

For $1{\leq}k{\leq}r$, let ${\sigma}$($K_{r,r}$ - ke, n) be the smallest even integer such that every n-term graphic sequence ${\pi}$ = ($d_1$, $d_2$, ..., $d_n$) with term sum ${\sigma}({\pi})$ = $d_1$ + $d_2$ + ${\cdots}$ + $d_n\;{\geq}\;{\sigma}$($K_{r,r}$ - ke, n) has a realization G containing $K_{r,r}$ - ke as a subgraph, where $K_{r,r}$ - ke is the graph obtained from the $r\;{\times}\;r$ complete bipartite graph $K_{r,r}$ by deleting k edges which form a matching. In this paper, we determine ${\sigma}$($K_{r,r}$ - ke, n) for even $r\;({\geq}4)$ and $n{\geq}7r^2+{\frac{1}{2}}r-22$ and for odd r (${\geq}5$) and $n{\geq}7r^2+9r-26$.

• The KIPS Transactions:PartD
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• v.10D no.7
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• pp.1189-1196
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• 2003

Owing to the developed If industry, many people are more and more interested in Workflow which is an automated business processing system. In this paper, we present basic structures and various parallel processing structures of a workflow using EMFG (Extended Mark Flow Graph) that makes conceptional design available. And then, We design a workflow with EMFG. We propose the commitability verification method to check whether a workflow can complete or not and the logical bug verification method to find whether invalid components exist or not by using simulation result of it. The proposed EMFG modeling and analysis method for a workflow make it possible to become a visual and formal design. Also, it makes intuitional and mathematical analysis possible.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.10a
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• pp.118-118
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• 1993

We consider a discrete event dynamic system called periodic job shop, where an identical mixture of items called minimal part set(MPS) is repetitively produced in the same processing order and the primary performance measure is the cycle time. The precedence relationships among events(starts of operations) are represented by a directed graph with rocurront otructure. When each operation starts as soon as all its preceding operations complete(called earliest starting), the occurrences of events are modeled in a linear system using a special algebra called minimax algebra. By investigating the eigenvalues and the eigenvectors, we develop conditions on the directed graph for which a stable steady state or a finite eigenvector exists. We demonstrate that each finite eigenvector, characterized as a finite linear combination of a class of eigenvalue, is the minimum among all the feasible schedules and an identical schedule pattern repeats every MPS. We develop an efficient algorithm to find a schedule among such schedules that minimizes a secondary performance measure related to work-in-process inventory. As a by-product of the linear system approach, we also propose a way of characterizing stable steady states of a class of discrete event dynamic systems.

• Journal of Electrical Engineering and Technology
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• v.3 no.3
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• pp.436-443
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• 2008

This paper presents a new method for building detection and reconstruction from aerial images. In our approach, we extract useful building location information from the generated disparity map to segment the interested objects and consequently reduce unnecessary line segments extracted in the low level feature extraction step. Hypothesis selection is carried out by using an undirected graph, in which close cycles represent complete rooftops hypotheses. We test the proposed method with the synthetic images generated from Avenches dataset of Ascona aerial images. The experiment result shows that the extracted 3D line segments of the reconstructed buildings have an average error of 1.69m and our method can be efficiently used for the task of building detection and reconstruction from aerial images.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1649-1654
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• 2014

A tournament T is an orientation of a complete graph and an arc in T is called pancyclic if it is contained in a cycle of length l for all $3{\leq}l{\leq}n$, where n is the cardinality of the vertex set of T. In 1994, Moon [5] introduced the graph parameter h(T) as the maximum number of pancyclic arcs contained in the same Hamiltonian cycle of T and showed that $h(T){\geq}3$ for all strong tournaments with $n{\geq}3$. Havet [4] later conjectured that $h(T){\geq}2k+1$ for all k-strong tournaments and proved the case k = 2. In 2005, Yeo [7] gave the lower bound $h(T){\geq}\frac{k+5}{2}$ for all k-strong tournaments T. In this note, we will improve his bound to $h(T){\geq}\frac{2k+7}{3}$.