• Korean Journal of Mathematics
• /
• v.29 no.4
• /
• pp.649-664
• /
• 2021

There have been numerous efforts to provide legal information to the general public easily. Most of the existing legal information services are based on keyword-oriented legal ontology. However, this keyword-oriented ontology construction has a sense of disparity from the relationship between the laws used together in actual cases. To solve this problem, it is necessary to study which laws are actually used together in various judicial precedents. However, this is difficult to implement with the existing methods used in computer science or law. In our study, we analyzed this by using topological data analysis, which has recently attracted attention very promisingly in the field of data analysis. In this paper, we applied the the Mapper algorithm, which is one of the topological data analysis techniques, to visualize the relationships that laws form organically in actual precedents.

• East Asian mathematical journal
• /
• v.34 no.2
• /
• pp.177-189
• /
• 2018

Recently, Topological Data Analysis (TDA) has attracted attention among various techniques for analyzing big data. Mapper algorithm, which is one of TDA techniques, is used to visualize the cluster diagram. In this study, students were clustered according to the characteristics and degree of mathematics anxiety using a mapper, and students were visualized according to mathematics anxiety. In order to do this, Mathematical Anxiety Scale (Ko & Yi, 2011) in the aspect of mathematical instability in terms of teaching - learning, ie, Nature of Mathematics, Learning Strategy, Test/Performance is used. And the number of questions that measure the anxiety of mathematics can be extracted by extracting the most relevant items among the items that measure the anxiety of mathematics.

• The Korean Journal of Applied Statistics
• /
• v.33 no.1
• /
• pp.75-86
• /
• 2020

Hotel review data can extract various information that includes purchasing factors that lead to consumption, advantages, and disadvantages for hotels. In particular, the sentiment keyword of the review data helps consumers understand the pros and cons of hotels. However, it is not efficient for consumers to read a large number of reviews. Therefore, it is necessary to offer a summary review to customers. In this study, we suggest providing summary information on sentiment keywords association as well as a network of hotels based on sentiment keywords. Based on a sentiment keyword dictionary, the extracted sentiment keywords associations construct the hotel network through topological data analysis based mapper. This hotel network allows a consumer to find some hotels associated with specific sentiment keywords as well as recommends the same related hotels. This summary information provides users with a summarized emotional assessment of hotels and helps hotel marketing teams understand consumers' perceptions of their hotel.

• Journal of the Korean Geographical Society
• /
• v.41 no.2 s.113
• /
• pp.188-194
• /
• 2006

Three-dimensional topological data is essential for 3D modeling and application such as emergency management and 3D network analysis. This paper reviewed current 3D topological data model and developed a method to construct 3D topological node-relation data structure from 2D computer aided design (CAD) data. The method needed two steps with medial axis-transformation and topological node-relation algorithms. Using a medial-axis transformation algorithm, the first step is to extract skeleton from wall data that was drawn polygon or double line in a CAD data. The second step is to build a topological node-relation structure by converting rooms to nodes and the relations between rooms to links. So, links represent adjacency and connectivity between nodes (rooms). As a result, with the conversion method 3D topological data for micro-level sub-unit of each building can be easily constructed from CAD data that are commonly used to design a building as a blueprint.

• Bulletin of the Korean Chemical Society
• /
• v.16 no.2
• /
• pp.169-180
• /
• 1995

A topological theory is introduced to extend Tsenoglou's theory to polymer blends having temporary and permanent networks composed of multicomponent polymers which have miscible and flexible chains. The topological theory may estimate the values of free elastic energy, the molecular weight between entanglements, and the equilibrium shear moduli, and it may establish more correctly the topological relations among these physical quantities. Through such introduction of the topological theory, there can be topologically analyzed the mixing law for the rubbery plateau modulus of a fluid polymer blend, and there can be considered the topological relationship to the equilibrium modulus of an interpenetrating polymer network containing trapped entanglements and dangling segments. The theoretically predictive values are compared and show good agreement with the experimental data for several miscible polymer blends.

• Spatial Information Research
• /
• v.18 no.5
• /
• pp.93-105
• /
• 2010

Spatial neighborhoods are spaces which are relate to target space. A 3D spatial query which is a function for searching spatial neighborhoods is a significant function in spatial analysis. Various methodologies have been proposed in related these studies, this study suggests an adjacent based methodology. The methodology of this paper implements topological data for represent a adjacency via using network based topological data model, then apply modifiable Dijkstra's algorithm to each topological data. Results of ordering analysis about an adjacent space from a target space were visualized and considered ways to take advantage of. Object of this paper is to implement a 3D spatial query for searching a target space with a adjacent relationship in 3D space. And purposes of this study are to 1)generate adjacency based 3D network data via network based topological data model and to 2)implement a 3D spatial query for searching spatial neighborhoods by applying Dijkstra's algorithms to these data.

• Bulletin of the Korean Chemical Society
• /
• v.16 no.3
• /
• pp.269-277
• /
• 1995

A topological theory has been introduced to extend the theory of Balsara and Nauman to evaluate the entropy of in homogeneous polymer solutions. Previous theories have considered only the terms about the displacement of junction points, while the present theory has obtained a more complete expression for the entropy by adding the topological interaction terms between strands. There have been predicted the characteristics of the spinodal decomposition and the interfacial tension of polymer solutions from the resultant expression. It is exposed that the theoretically predictive values show good agreement with the experimental data for polymer solutions.

• Journal of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1079-1101
• /
• 2020

This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a levelset curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1996.04a
• /
• pp.100-103
• /
• 1996

Presented in this study is an algorithmic procedure to obtain polyhedral model from a compound surface. The compound surface in this study denotes a collection of trimmed surfaces without topological relations. The procedure consists of two main modules: CAD data interface, and surface conversion to polyhedral model. The interface module gets geometric information from CAD databases, and makes topological information by scanning the geometric information. We are investigating CATIA system as a data source system. In the surface conversion module, a shell(compound surface with topological information) is approximated to a triangular-faceted polyhedral surface model through node sampling and triangulation steps. The obtained polyhedral model should obey the vertex-to-vertex rule and meet tolerance requirements. Since the polyhedral model has a simple data structure and geometry processing for it is very efficient and robust, the polyhedral model can be used in various applications, such as surface rendering in computer graphics, FEM model for engineering analysis, CAPP for surface machining, data generation for SLA, and NC tool path generation.

• Proceedings of the KSRS Conference
• /
• 2002.10a
• /
• pp.128-132
• /
• 2002

One of the fundamental components important to the analysis of spatial objects is to represent topological relationships between spatial features. Users of geographic information systems retrieve a lot of objects from spatial database and analyze their condition by means of topological relationships. The existing methods that represent these relationships have the disadvantage that they have limited information in $R^2$. In this paper, we represent and define the topological relationships between 3-dimensional spatial objects using the several representing methods of 2-dimensional features. We use the diverse representing methods, which include the 4-, 9-intersection, dimension extended and calculus-based method. Furthermore, we discuss OGC's topological relationships and operators for 3-dimensional spatial data.