• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.507-519
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• 2017

We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.671-677
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• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• ETRI Journal
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• v.29 no.3
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• pp.381-389
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• 2007

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ${\rho}$)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.10C
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• pp.1363-1369
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• 2004

LDPC(Low Density Parity Check) codes are described by bipartite graphs with bit nodes and parity-check nodes. Tanner derived minimum distance bounds of the regular LDPC code in terms of the eigenvalues of the associated adjacency matrix. In this paper we generalize the Tanner's results. We derive minimum distance bounds applicable to both regular and blockwise-irregular LDPC codes. The first bound considers the relation between bit nodes in a minimum-weight codeword, and the second one considers the connectivity between parity nodes adjacent to a minimum-weight codeword. The derived bounds make it possible to describe the distance property of the code in terms of the eigenvalues of the associated matrix.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.9
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• pp.514-526
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• 2004

Microarray is a new technique for gene expression experiment, which has gained biologist's attention for recent years. This technology enables us to obtain hundreds and thousands of expression of gene or genotype at once using microarray Since it requires manual work to analyze patterns of gene expression, we want to develop an effective and automated tools to analyze microarray image. However it is difficult to analyze DNA chip images automatically due to several problems such as the variation of spot position, the irregularity of spot shape and size, and sample contamination. Especially, one of the most difficult problems in microarray analysis is the block and spot addressing, which is performed by manual or semi automated work in all the commercial tools. In this paper we propose a new algorithm to address the position of spot and block using a new concept of regular structure grid searching. In our algorithm, first we construct maximal I-regular sequences from the set of input points. Secondly we calculate the rotational angle and unit distance. Finally, we construct I-regularity graph by allowing pseudo points and then we compute the spot/block address using this graph. Experiment results showed that our algorithm is highly robust and reliable. Supplement information is available on http://jade.cs.pusan.ac.kr/~autogrid.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1371-1374
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• 2002

This paper compares four network con-figurations for using as the logical topology in multi- hop wavelength division multiplexing (WDM) networks. The regular network configurations studied in this paper axe ShuffleNet, de Bruijn graph, hypercube, and Man-hattan street network. Instead of using the weight mean hop distance of node placement problem for comparing optimum logical topology, we introduce a new objective function that includes h and the network cost. It can be seen that the network cost strongly depends on the logical topology selected for the implementation of the network. The objective of this paper is to find an optimum logical topology for WDM networks that gives low as well as low network cost.

• Journal of Wetlands Research
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• v.15 no.3
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• pp.397-406
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• 2013

Wetland conservation plan has been established to protect ecologically important wetlands based on vegetation integrity, spatial distribution of endangered species, but recently more demands are concentrated on the landscape ecological approaches such as topological relationship, neighboring area, spatial arrangements between wetlands at the broad scale. Landscape ecological analysis and graph theory are conducted to identify spatial characteristics related to core nodes and weak links of wetland networks in Nakdong basin. Regular planar model, which is selected for wetland networks, is applied in the Nakdong basin. The analysis indicates that 5 regional groups and 4 core wetlands are extracted with 15km threshold distance. The IIC and PC values based on the binary and probability models suggest that the wetland group C composed of main stream of Nakdong river and Geumho river is the most important area for wetland network. Wetland conservation plan, restoration projected of damaged and weak links between wetlands should be proposed through evaluating the node, links, and networks from wetlands at the local to the regional scale in Nakdong basin.

• Journal of the HCI Society of Korea
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• v.5 no.2
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• pp.1-6
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• 2010

In this research, we designed the head mouse system for disabled and gamers, a mouse controller which can be controlled by head movements and eye blinks only, and compared its performance with other regular mouse controller systems. The head mouse was moved by a gyro-sensor, which can measure an angular rotation of a head movement, and the eye blink was used as a clicking event of the mouse system. Accumulated errors caused by integral, which was a problem that previous head mouse system had, were removed periodically, and treated as dead zones in the non-linear relative point graph, and direct mouse point control was possible using its moving distance and acceleration calculation. We used the active light sources to minimize the influence of the ambient light changes, so that the head mouse was not affected by the change in external light source. In a comparison between the head mouse and the gazing tracking mouse (Quick Glance), the above method resulted about 21% higher score on the clicking event experiment called "20 clicks", about 25% higher on the dasher experiment, and about 37% higher on on-screen keyboard test respectively, which concludes that the proposed head mouse has better performance than the standard mouse system.