• Journal of Korea Spatial Information System Society
• /
• v.3 no.1 s.5
• /
• pp.49-62
• /
• 2001

Recently, component-based software has become main trends in designing and developing computer software products. This component-based software has advantage of the interoperability on distributed computing environment and the reusability of pre-developed components. Also, GIS is designed and implemented with this component-based methodology, called Open GIS Component. OGC(OpenGIS Consortium) have announced various implementation and design specification and topic in GIS. In GIS, Spatial analysis functions like network analysis, TIN analysis are very important function and basically, estimate system functionality and performance using this analysis methods. The simple feature geometry specification is announced by OGC to increase the full interoperability of various spatial data. This specification includes just geometry spatial data model. However, in GIS which manages spatial data, not only geometric data but also topological data and various analysis functions have been used. The performance of GIS depends on how this geometric and topological data is managed well and how various spatial analyses are executed efficiently. So it requires integrated spatial data model between geometry and topology and extended data model of topology for spatial analysis, in case network analysis and TIN analysis in open GIS component. In this paper, we design analysis component like network analysis component and TIN analysis component. To manage topological information for spatial analysis in open GIS component, we design extended data model of simple feature geometry for spatial analysis. In addition to, we design the overall system architecture of open GIS component contained this topology model for spatial analysis.

• Journal of the Korean housing association
• /
• v.22 no.2
• /
• pp.101-109
• /
• 2011

Until now, several comparative approaches were developed within the studies of Korean, Chinese, and Japanese traditional housings. In those studies, however, each space in the traditional houses was only treated in individual and fragmentary manners, and they lacked the interpretation of the topological attribute of each space within a holistic structure organized by unit spaces, and of the cultural-behavioral meaning of them within a holistic space-use pattern of the housing. The topological attribute and behavioral meaning can be analyzed and interpreted with the quantitative spatial analysis method such as Space Syntax. This study aims to analyze the traditional housings in Korea, China and Japan in the holistic aspect of spatial structure using Space Syntax, and to compare the analysis results with relating the structural attributes to the space-use pattern. In this study, the 'Banga' in Chosun era, the 'Siheyuan' in Ming-Ching era, and the 'Shoinzukuri' in Edo era were selected as the analysis subjects. The integration indices were calculated from the convex maps representing the subjects, and the common and different attributes of the three subjects were defined through comparative analyses.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.296-311
• /
• 2021

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.4
• /
• pp.324-341
• /
• 2023

Topological data analysis (TDA) is a data analysis technique, recently developed, that investigates the overall shape of a given dataset. The mapper algorithm is a TDA method that considers the connectivity of the given data and converts the data into a mapper graph. Compared to persistent homology, another popular TDA tool, that mainly focuses on the homological structure of the given data, the mapper algorithm is more of a visualization method that represents the given data as a graph in a lower dimension. As it visualizes the overall data connectivity, it could be used as a prediction method that visualizes the new input points on the mapper graph. The existing mapper packages such as Giotto-TDA, Gudhi and Kepler Mapper provide the descriptive mapper algorithm, that is, the final output of those packages is mainly the mapper graph. In this paper, we develop a simple predictive algorithm. That is, the proposed algorithm identifies the node information within the established mapper graph associated with the new emerging data point. By checking the feature of the detected nodes, such as the anomality of the identified nodes, we can determine the feature of the new input data point. As an example, we employ the fraud credit card transaction data and provide an example that shows how the developed algorithm can be used as a node prediction method.

• The KIPS Transactions:PartA
• /
• v.14A no.5
• /
• pp.263-268
• /
• 2007

In this paper, we analyze some topological properties of Folded Hyper-Star FHS(2n,n). First, we prove that FHS(2n,n) has maximal fault tolerance, and broadcasting time using double rooted spanning tree is 2n-1. Also we show that FHS(2n,n) can be embedded into Folded hypercube with dilation 1, and Folded hypercube can be embedded into FHS(2n,n) ith dilation 2 and congestion 1.

• Korean Journal of Computational Design and Engineering
• /
• v.5 no.4
• /
• pp.293-300
• /
• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• The Transactions of the Korean Institute of Electrical Engineers B
• /
• v.50 no.2
• /
• pp.79-85
• /
• 2001

In this paper, a novel Zero-Current-Transition (ZCT) technique, which provides Zero-Current-Switching (ZCS) turn-off of the main switch, the main diode and the auxiliary switch, is presented. The proposed auxiliary circuit consists of minimum elements only one auxiliary switch, resonant inductor and resonant capacitor. Also the reduced di/dt, which is obtained by resonant inductor, helps soft turn-on of the main switch. Besides, to eliminate the additional conduction loss and current stress on main switch, a topological variation was performed. The theoretical analysis and the operation principle of the new ZCT techniques are described in detail with a boost converter as an example. To verify the validity of the proposed ZCT techniques, the simulation and the experiment were performed under 1kW output power and 100kHz switching frequency.

• Bulletin of the Korean Chemical Society
• /
• v.16 no.11
• /
• pp.1046-1056
• /
• 1995

A topological theory has been introduced to evaluate the degree of complexation and the viscosity of polymer complexes by extending the theory of Iliopoulos and Audebert for aqueous polymer solutions. The previous theory of Iliopoulos and Audebert has offered only a semiquantitative theoretical model for polymer complex systems, whereas our present work gives a general theoretical model applicable to all the polymer complex systems. Their theories considered only the physical property term caused by the displacement of complexed points between polymer solute chains, while our theory deals with all the physical effects, caused by the displacement of complexed points entangled points in polymer solute chains. There have been predicted the characteristics of physical properties from the expression. It is exposed that the predictive values show good agreement with the experimental data for polymer complexes.

• Bulletin of the Korean Chemical Society
• /
• v.17 no.3
• /
• pp.245-253
• /
• 1996

A topological theory has been introduced to explain and evaluate the fractional volumes of system materials, the change of the weight and concentration of monomer molecules, molecular weight distribution, and interaction functions of polymer-polymer and polymer-oligomer, etc. for dispersion polymerization. The previous theory of Lu et al. has offered only an incomplete simulation model for dispersion polymer systems, whereas our present one gives a general theoretical model applicable to all the polymerization systems. The theory of Lu et al. considered only the physical property term caused by interaction between matters of low molecular weight (i.e., diluent, monomer, and oligomer) and polymer particles without dealing with physical properties caused by the structure of polymer networks in polymer particles, while our theory deals with all physical effect possible, caused by the displacement of not only entangled points but also junction points in polymer particles. The theoretically predictive values show good agreement with the experimental data for dispersion polymerization systems.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.839-853
• /
• 2022

We define the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.