• Journal of Korea Multimedia Society
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• v.21 no.1
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• pp.10-17
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• 2018

Persistence Betty numbers, which are the rank of the persistent homology, are a generalized version of the size theory widely known as a descriptor for shape analysis. They show robustness to both perturbations of the topological space that represents the object, and perturbations of the function that measures the shape properties of the object. In this paper, we present a shape matching algorithm which is based on the use of persistence Betty numbers. Experimental tests are performed with Kimia dataset to show the effectiveness of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2800-2811
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• 1996

The deformation of a structure shall be called homologous, if a given geometrical relation holds, for a given number of structural points, before, during, and after the deformation. Some researchers have utilized the idea on structural design with finite element method. The approaches use the decomposition of the FEM equation or equality of eqality equations to obtain homologous deformation. However, weight reduction and response constraints such as stress, displacement or natural frequency cannot be considered by those theories. An optimization method solving the above problems is suggested to gain homologous deformation. Homology constraints can be considered under multiple loadindg conditions as well as a single loading condition. Homology index is defined for the multiple loading conditions Examples are solved to present the performances of the method.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.175-183
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• 2010

The classical group completion theorem states that under a certain condition the homology of ${\Omega}BM$ is computed by inverting ${\pi}_0M$ in the homology of M. McDuff and Segal extended this theorem in terms of homology fibration. Recently, more general group completion theorem for simplicial spaces was developed. In this paper, we construct a symmetric monoidal 2-category ${\mathcal{A}}$. The 1-morphisms of ${\mathcal{A}}$ are generated by three atomic 2-dimensional CW-complexes and the set of 2-morphisms is given by the group of path components of the space of homotopy equivalences of 1-morphisms. The main part of the paper is to compute the homotopy type of the group completion of the classifying space of ${\mathcal{A}}$, which is shown to be homotopy equivalent to ${\mathbb{Z}}{\times}BAut^+_{\infty}$.

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.234-240
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• 2014

C-C chemokine receptor type 4 (CCR4) is a chemokine receptor with seven transmembrane helices and it belongs to the GPCR family. It plays an important role in asthma, lung disease, atopic dermatitis, allergic bronchopulmonary aspergillosis, cancer, inflammatory bowel disease, the mosquito-borne tropical diseases, such as dengue fever and allergic rhinitis. Because of its role in wide spectrum of disease processes, CCR4 is considered to be an important drug target. Three dimensional structure of the protein is essential to determine the functions. In the present study homology modeling of human CCR4 was performed based on crystal structure of CCR5 chemokine receptor. The generated models were validated using various parameters. Among the generated homology models the best one is selected based on validation result. The model can be used for performing further docking studies to identifying the critical interacting residues.

• Journal of Integrative Natural Science
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• v.6 no.1
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• pp.16-20
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• 2013

G-protein-coupled receptor (GPCR) superfamily is the largest known receptor family, characterized by seven transmembrane domains and considered to be an important drug target. In this study we focused on an orphan GPCR termed as GPR18. As there is no X-ray crystal structure has been reported for this receptor, we report on a homology model of GPR18. Template structure with high homology was used for modeling and ten models were developed. A model was selected and refined by energy minimization. The selected model was further validated using various parameters. Our results could be a starting point for further structure based drug design.

• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.35-40
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• 2016

Protein phosphatase manganese dependent 1D (PPM1D) is one of the Ser/Thr protein phosphatases belongs to the PP2C family. They play an important role in cancer tumorigenesis of various tumors including neuroblastoma, pancreatic adenocarcinoma, medulloblastoma, breast cancer, prostate cancer and ovarian cancer. Even though PPM1D is involved in the pathophysiology of various tumors, the three dimensional protein structure is still unknown. Hence in the present study, homology modelling of PPM1D was performed. 20 different models were modelled using single- and multiple-template based homology modelling and validated using different techniques. Best models were selected based on the validation. Three models were selected and found to have similar structures. The predicted models may be useful as a tool in studying the pathophysiological role of PPM1D.

• Journal of Korea Multimedia Society
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• v.22 no.1
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• pp.18-26
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• 2019

In this paper we propose how to detect circular objects in the gray scale image and segment them using the discrete Morse theory, which makes it possible to analyze the topology of a digital image, when it is transformed into the data structure of some combinatorial complex. It is possible to get meaningful information about how many connected components and topologically circular shapes are in the image by computing the persistent homology of the filtration using the Morse complex. We obtain a Morse complex by modeling an image as a cubical cellular complex. Each cell in the Morse complex is the critical point at which the topological structure changes in the filtration consisting of the level sets of the image. In this paper, we implement the proposed algorithm of segmenting the circularly shaped objects with a long persistence of homology as well as computing persistent homology along the filtration of the input image and displaying in the form of a persistence diagram.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.399-408
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• 2006

The action of mapping class groups of a handlebody on the first homology group is investigated. A homological analogy of mapping class groups of a handlebody is defined and its system of generators is given.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.173-179
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• 1996

M be an ($n\geq3$)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n ＋ 2)-dimensional sphere $S^{n＋2}$(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.63-75
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• 2006

We study the homology of based gauge groups associated with the principal Spin(n) bundles over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the Dyer-Lash of operations.