• Honam Mathematical Journal
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• v.27 no.1
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.5
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• pp.1149-1160
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• 2005

Generally, the network topology design problem, which is difficult to solve with the classical method because it has exponentially increasing complexity with the augmented network size, is characterized as a kind of NP-hard combinatorial optimization problem. The problem of this research is to design the highly reliable network topology considering the connection cost and all-terminal network reliability, which can be defined as the probability that every pair of nodes can communicate with each other. In order to solve the highly reliable network topology design problem minimizing the construction cost subject to network reliability, we proposes an efficient two phase approach to design reliable network topology, i.e., the first phase employs, a genetic algorithm (GA) which uses $Pr\ddot{u}fer$ number for encoding method and backtracking Algorithm for network reliability calculation, to find the spanning tree; the second phase is a greedy method which searches the optimal network topology based on the spanning ree obtained in the first phase, with considering 2-connectivity. finally, we show some experiments to demonstrate the effectiveness and efficiency of our two phase approach.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.8
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• pp.755-760
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• 2015

For proper wound healing, dermal contraction and remodeling are critical; during the natural healing process, differentiated fibroblasts called "myofibroblasts" typically undertake these functions. For severe wounds, however, a critical mass of dermal matrix and fibroblasts are lost, making self-regeneration impossible. To overcome this impairment, synthetic wound patches with embedded functional cells can be used to promote healing. In this study, we developed a polydioxanone (PDO)-based cell-embedded sheet on which dermal fibroblasts were cultured and induced for differentiation into myofibroblasts, whereby the following combinatorial physicochemical stimuli were also applied: aligned topology, electric field (EF), and growth factor. The results show that both the aligned topology and EF synergistically enhanced the expression of alpha smooth-muscle actin (${\alpha}$-SMA), a key myofibroblast marker. Our proof-of-concept (POC) experiments demonstrated the potential applicability of a myofibroblast-embedded PDO sheet as a wound patch.

• Proceedings of the KIEE Conference
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• 2000.07a
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• pp.537-540
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• 2000

The Distribution System consist of many tie-line switches and sectionalizing switches, operated a radial type. When an outage occurs in Distribution System, outage areas are isolated by system switches, has to restored as soon as possible. At this time, system operator have to get a information about network topology for service restoration of outage areas. Therefore, the searching result of restorative topology has to fast computation time and reliable result topology for to restore a electric service to outage areas, equal to optimal switching operation problem. So, the problem can be defined as combinatorial optimization problem. The service restoration problem is so important problem which have outage area minimization, outage loss minimization. Many researcher is applying to the service restoration problem with various techniques. In this paper, advanced Dijkstra algorithm is applied to searching a restoration topology, is so efficient to searching a shortest path in graph type network. Additionally, fuzzy rules and operator are applied to overcome a fuzziness of correlation with input data. The present technique has superior results which are fast computation time and searching results than previous researches, demonstrated by example distribution model system which has 3 feeders, 26 buses. For a application capability to real distribution system, additionally demonstrated by real distribution system of KEPCO(Korea Electric Power Corporation) which has 8 feeders and 140 buses.

• Journal of Korea Multimedia Society
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• v.16 no.4
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• pp.472-482
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• 2013

This paper proposes a wireless LAN topology configuration method for enhancing indoor location-awareness and improving network performance simultaneously. We first develop four objective functions that yield objective goals significant to the optimal design of a wireless LAN topology in terms of location-awareness accuracy and network performance factors. Then, we develop metaheuristic algorithms such as simulated annealing, tabu search, and genetic algorithm that examine the proposed objective functions and generate a near-optimal solution for a given objective function. Finally, four objective functions and metaheuristic algorithms developed in this paper are exploited to evaluate and measure the performance of the proposed wireless LAN topology configuration method.

• Journal of KIISE:Software and Applications
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• v.32 no.4
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• pp.247-257
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• 2005

Generally, the network topology design problem is characterized as a kind of NP-hard combinatorial optimization problem, which is difficult to solve with the classical method because it has exponentially increasing complexity with the augmented network size. In this paper, we propose the efficient approach with two phase that is comprised of evolutionary computation approach based on Prufer number(PN), which can efficiently represent the spanning tree, and a heuristic method considering 2-connectivity, to solve the highly reliable network topology design problem minimizing the construction cost subject to network reliability: firstly, to find the spanning tree, genetic algorithm that is the most widely known type of evolutionary computation approach, is used; secondly, a heuristic method is employed, in order to search the optimal network topology based on the spanning tree obtained in the first Phase, considering 2-connectivity. Lastly, the performance of our approach is provided from the results of numerical examples.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.553-563
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• 2017

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1265-1283
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• 2019

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.4
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• pp.10-18
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• 2002

Network topology design is a multiobjective problem with various design components. The components such as cost, message delay and reliability are important to gain the best performance. Recently, Genetic Algorithms(GAs) have been widely used as an optimization method for real-world problems such as combinatorial optimization, network topology design, and so on. This paper proposed a method of Multi-objective GA for Design of the network topology which is to minimize connection cost and message delay time. A common difficulty in multiobjective optimization is the existence of an objective conflict. We used the prufer number and cluster string for encoding, parato elimination method and niche-formation method for the fitness sharing method, and reformation elitism for the prevention of pre-convergence. From the simulation, the proposed method shows that the better candidates of network architecture can be found.

• ETRI Journal
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• v.39 no.1
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• pp.1-12
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• 2017

In this paper, we present a new approach for the progressive compression of three-dimensional (3D) mesh geometry using redundant frame dictionaries and sparse approximation techniques. We construct the proposed frames from redundant linear combinations of the eigenvectors of a combinatorial mesh Laplacian matrix. We achieve a sparse synthesis of the mesh geometry by selecting atoms from a frame using matching pursuit. Experimental results show that the resulting rate-distortion performance compares favorably with other progressive mesh compression algorithms in the same category, even when a very simple, sub-optimal encoding strategy is used for the transmitted data. The proposed frames also have the desirable property of being able to be applied directly to a manifold mesh having arbitrary topology and connectivity types; thus, no initial remeshing is required and the original mesh connectivity is preserved.