• Journal of the Economic Geographical Society of Korea
• /
• v.15 no.3
• /
• pp.343-357
• /
• 2012

The Seoul metropolitan subway system can be represented by a graph which consists of nodes and edges. In this paper, we study classification of subway stations and trip behaviour of subway passengers through partitioning the graph of the subway system into roughly equal groups. A weight of each edge of the graph is set to the number of passengers who pass the edge, where the number of passengers is extracted from the transportation card transaction database. Since the graph partitioning problem is NP-complete, we propose a heuristic algorithm to partition the subway graph. The heuristic algorithm uses one of two alternative objective functions, one of which is to minimize the sum of weights of edges connecting nodes in different groups and the other is to maximize the ratio of passengers who get on the subway train at one subway station and get off at another subway station in the same group to the total subway passengers. In the experimental results, we illustrate the subway stations and edges in each group by color on a map and analyze the trip behaviour of subway passengers by the group origin-destination matrix.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.24 no.1
• /
• pp.37-42
• /
• 2024

This paper suggests polynomial time algorithm for cutwidth minimization problem that classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. To find the minimum cutwidth CW_f(G)=max_𝜈∈_VCW_f(𝜈)for given graph G=(V,E),m=｜V｜, n=｜E｜, the proposed algorithm divides neighborhood N_G[𝜈_i] of the maximum degree vertex 𝜈_i in graph G into left and right and decides the vertical cut plane with minimum number of edges pass through the vertex 𝜈_i firstly. Then, we split the left and right N_G[𝜈_i] into horizontal sections with minimum pass through edges. Secondly, the inner-section vertices are connected into line graph and the inter-section lines are connected by one line layout. Finally, we perform the optimization process in order to obtain the minimum cutwidth using vertex moving method. Though the proposed algorithm requires O(n²) time complexity, that can be obtains the optimal solutions for all of various experimental data

• Journal of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.709-723
• /
• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.8 no.3
• /
• pp.119-128
• /
• 1988

The purpose of this research is to quantify the effects of water content(0.3~1.255%) and temperature ($4{\sim}40^{\circ}C$) on the equilibrium distribution of toxic organic pollutant in unsaturated soil. The priority pollutants, Dichloromethane and 1, 1, 1-Trichloroethane were selected as toxic organic pollutants and the Korean decomposed granite soil as the experimental soil media. Two models were developed on the basis of shapes of soil water distribution in unsaturated soil and compared; complete surface coating(model I) vs. spot clustering (model II). From the experiment, a large decrease in the values of effective partition coefficient ($K_{eff}$) was observed as the water content increased. As the temperature increased, the $K_{eff}$ values decreased, and this effect was magnified at lower water contents. The values of $K_{eff}$ were correlated better with the estimated values using model II. Thus it was experimentally proved that the soil water tends to enclose the soil grain partly at lower water contents.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.4
• /
• pp.1712-1731
• /
• 2016

In this paper, we propose a novel saliency detection framework via multiple random walks (MRW) which simulate multiple agents on a graph simultaneously. In the MRW system, two agents, which represent the seeds of background and foreground, traverse the graph according to a transition matrix, and interact with each other to achieve a state of equilibrium. The proposed algorithm is divided into three steps. First, an initial segmentation is performed to partition an input image into homogeneous regions (i.e., superpixels) for saliency computation. Based on the regions of image, we construct a graph that the nodes correspond to the superpixels in the image, and the edges between neighboring nodes represent the similarities of the corresponding superpixels. Second, to generate the seeds of background, we first filter out one of the four boundaries that most unlikely belong to the background. The superpixels on each of the three remaining sides of the image will be labeled as the seeds of background. To generate the seeds of foreground, we utilize the center prior that foreground objects tend to appear near the image center. In last step, the seeds of foreground and background are treated as two different agents in multiple random walkers to complete the process of salient object detection. Experimental results on three benchmark databases demonstrate the proposed method performs well when it against the state-of-the-art methods in terms of accuracy and robustness.

• Journal for History of Mathematics
• /
• v.19 no.2
• /
• pp.1-24
• /
• 2006

We study the theory of finite series in Chosun Dynasty Mathematics. We divide it into two parts by the publication of Lee Sang Hyuk(李尙爀, 1810-?)'s Ik San(翼算, 1868) and then investigate their history. The first part is examined by Gyung Sun Jing(慶善徵, 1616-?)'s Muk Sa Jib San Bub(默思集算法), Choi Suk Jung(崔錫鼎)'s Gu Su Ryak(九數略), Hong Jung Ha(洪正夏)'s Gu Il Jib(九一集), Cho Tae Gu(趙泰耉)'s Ju Su Gwan Gyun(籌書管見), Hwang Yun Suk(黃胤錫)'s San Hak Ib Mun(算學入門), Bae Sang Sul(裵相設)'s Su Gye Soe Rok and Nam Byung Gil(南秉吉), 1820-1869)'s San Hak Jung Ei(算學正義, 1867), and then conclude that the theory of finite series in the period is rather stable. Lee Sang Hyuk obtained the most creative results on the theory in his Ik San if not in whole mathematics in Chosun Dynasty. He introduced a new problem of truncated series(截積). By a new method, called the partition method(分積法), he completely solved the problem and further obtained the complete structure of finite series.

• Journal of Technology Innovation
• /
• v.17 no.2
• /
• pp.1-23
• /
• 2009

The Survey on the Industrial Research and Development(R&D) is the primary source of information on R&D performed by Korea industrial sector. The results of the survey are used to assess trends in R&D expenditures. Government agencies, corporations, and research organizations use the data to investigate productivity determinants, formulate tax policy, and compare individual company performance with industry averages. Recently, Korea Industrial Technology Association(KOITA) has collected the data by complete enumeration. Koita has, currently, considered sample survey because the number of R&D institutions in industry has been dramatically increased. This study develops survey design for the industrial research and development(R&D) statistics by introducing a sample survey. Companies are divided into 8 groups according to the amount of R&D expenditures and firm size or type. We collect the sample from 24 or 8 sampling strata and compare the results with those of complete enumeration survey. The estimates from 24 sampling strata are not significantly different to the results of complete enumeration survey. We propose the survey design as follows: Companies are divided into 11 groups including the companies of which R&D expenditures are unknown. All large companies are included in the survey and medium and small companies are sampled from 70% and 3%. Simple random sampling (SRS) is applied to the small company partition since they show uniform distribution in R&D expenditures. The independent probability proportionate to size (PPS) sampling procedure may be applied to those companies identified as 'not R&D performers'. When respondents do not provide the requested information, estimates for the missing data are made using imputation algorithms. In the future study, new key variables should be developed in survey questionnaires.

• Journal of Elementary Mathematics Education in Korea
• /
• v.15 no.1
• /
• pp.199-219
• /
• 2011

In this thesis, we designed a experimental learning-teaching plan of 'decimal fraction concept' at the 4-th grade level. We rest our plan on two basic premises. One is the fact that a essential concept of decimal fraction is 'polynomial of which indeterminate is 10', and another is the fact that the origin of decimal fraction is successive measurement activities which improving accuracy through decimal partition of measuring unit. The main features of our experimental learning-teaching plan is as follows. Firstly, students can experience a operation which generate decimal unit system through decimal partitioning of measuring unit. Secondly, the decimal fraction expansion will be initially introduced and the complete representation of decimal fraction according to positional notation will follow. Thirdly, such various interpretations of decimal fraction as 3.751m, 3m+7dm+5cm+1mm, $(3+\frac{7}{10}+\frac{5}{100}+\frac{1}{1000})m$ and $\frac{3751}{1000}m$ will be handled. Fourthly, decimal fraction will not be introduced with 'unit decimal fraction' such as 0.1, 0.01, 0.001, ${\cdots}$ but with 'natural number+decimal fraction' such as 2.345. Fifthly, we arranged a numeration activity ruled by random unit system previous to formal representation ruled by decimal positional notation. A experimental learning-teaching plan which presented in this thesis must be examined through teaching experiment. It is necessary to successive research for this task.

• Journal of the Society of Disaster Information
• /
• v.15 no.4
• /
• pp.524-530
• /
• 2019

Purpose: In this paper, we construct a detailed three-dimensional interface element using a three-dimensional analysis program, and evaluate the composite behavior stability of the connector by applying physical properties such as the characteristics of general members and those of reinforced members Method: The analytical model uses solid elements, including non-linear material behavior, to complete the modeling of beam structures, circular flanges, bolting systems, etc. to the same dimensions as the design drawing, with each member assembled into one composite behavior linkage. In order to more effectively control the uniformity and mesh generation of other element type contact surfaces, the partitioning was performed. Modeled with 50 carbon steel materials. Results: It shows the displacement, deformation, and stress state of each load stage by the contact adjoining part, load loading part, fixed end part, and vulnerable anticipated part by member, and after displacement, deformation, The effect of the stress distribution was verified and the validity of the design was verified. Conclusion: Therefore, if the design support of the micro pile is determined based on this result, it is possible to identify the Vulnerable Parts of the composite behavior connector and the degree of reinforcement.

• Journal of the Korea Society of Computer and Information
• /
• v.27 no.2
• /
• pp.43-51
• /
• 2022

In this paper, we suggest the method to improve the existing method leaning context-free grammar(CFG) using tabular representation(TBL) as a chromosome of genetic algorithm in grammatical inference and show the more efficient experimental result. We have two improvements. The first is to improve the formula to reflect the learning evaluation of positive and negative examples at the same time for the fitness function. The second is to classify partitions corresponding to TBLs generated from positive learning examples according to the size of the learning string, proceed with the evolution process by class, and adjust the composition ratio according to the success rate to apply the learning method linked to survival in the next generation. These improvements provide better efficiency than the existing method by solving the complexity and difficulty in the crossover and generalization steps between several individuals according to the size of the learning examples. We experiment with the languages proposed in the existing method, and the results show a rather fast generation rate that takes fewer generations to complete learning with the same success rate than the existing method. In the future, this method can be tried for extended CYK, and furthermore, it suggests the possibility of being applied to more complex parsing tables.