• Journal of computational fluids engineering
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• v.9 no.4
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• pp.20-33
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• 2004

In this study a stretching-mapping method is proposed for calculating the materials' stretching exponents, which are to be used in quantification of the mixing effect. In this method, the mapping tensor associated with the deformation of each fluid material is first obtained. Then deformations of a lot of materials are obtained by applying the mapping tensor. The local stretching rates and their space-average values are next computed with the mapped deformations. Application to a simple time-periodic flow within a cavity shows that the method is indeed effective compared with the conventional method; i.e. the mapping method is fast and yields the same results as the conventional one.

• Applied Microscopy
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• v.46 no.4
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• pp.179-183
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• 2016

Mapping brain structural and functional connections through the whole brain is essential for understanding brain mechanisms and the physiological bases of brain diseases. Although region specific structural or functional deficits cause brain diseases, the changes of interregional connections could also be important factors of brain diseases. This review will introduce common neuroimaging modalities, including structural magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion tensor imaging, and other recent neuroimaging analyses methods, such as voxel-based morphometry, cortical thickness analysis, local gyrification index, and shape analysis for structural imaging. Tract-Based Spatial Statistics, TRActs Constrained by UnderLying Anatomy for diffusion MRI, and independent component analysis for fMRI also will also be introduced.

• Proceedings of the Korean Society of Medical Physics Conference
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• 2006.08a
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• pp.147-147
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• 2006

• Korean Journal of Radiology
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• v.24 no.6
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• pp.553-563
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• 2023

Objective: Functional magnetic resonance imaging (fMRI) and diffusion tensor imaging-derived tractography (DTI-t) contribute to the localization of language areas, but their accuracy remains controversial. This study aimed to investigate the diagnostic performance of preoperative fMRI and DTI-t obtained with a simultaneous multi-slice technique using intraoperative direct cortical stimulation (DCS) or corticocortical evoked potential (CCEP) as reference standards. Materials and Methods: This prospective study included 26 patients (23-74 years; male:female, 13:13) with tumors in the vicinity of Broca's area who underwent preoperative fMRI and DTI-t. A site-by-site comparison between preoperative (fMRI and DTI-t) and intraoperative language mapping (DCS or CCEP) was performed for 226 cortical sites to calculate the sensitivity and specificity of fMRI and DTI-t for mapping Broca's areas. For sites with positive signals on fMRI or DTI-t, the true-positive rate (TPR) was calculated based on the concordance and discordance between fMRI and DTI-t. Results: Among 226 cortical sites, DCS was performed in 100 sites and CCEP was performed in 166 sites. The specificities of fMRI and DTI-t ranged from 72.4% (63/87) to 96.8% (122/126), respectively. The sensitivities of fMRI (except for verb generation) and DTI-t were 69.2% (9/13) to 92.3% (12/13) with DCS as the reference standard, and 40.0% (16/40) or lower with CCEP as the reference standard. For sites with preoperative fMRI or DTI-t positivity (n = 82), the TPR was high when fMRI and DTI-t were concordant (81.2% and 100% using DCS and CCEP, respectively, as the reference standards) and low when fMRI and DTI-t were discordant (≤ 24.2%). Conclusion: fMRI and DTI-t are sensitive and specific for mapping Broca's area compared with DCS and specific but insensitive compared with CCEP. A site with a positive signal on both fMRI and DTI-t represents a high probability of being an essential language area.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• The Journal of Engineering Geology
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• v.2 no.2
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• pp.155-165
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• 1992

The purpose of this study is to evaluate compatability of seismic source characteristics of the Kern County earthquake to those of Korean Peninsula seismotectonics. The compatability could be used to make Korean type response spectrum from the strong ground motions observed from the assingned earthquake. The July 21, 1952, Kern County, California, earthquake is the largest earthquake to occur in the western U.S. since 1906, and the repeat of this event poses a significant seismic hazard. The Kern County event was a complex thrusting event, with a surface rupture pattern that varied from pure leftlateral strike-slip to pure dip-slip. A time dependent moment tensor inversion was applied to ten observed teleseismic long-period body waves to investigate the source complexity. Since a conventional moment tensor inversion(constant geometry through time) returns a non-double-couple source when the seismic source changes(fault orientation and direction of slip) with time, we are required to use the time dependent moment tensor which allows a first-order mapping of the geometric and temporal complexity. From the moment tensor inversion, a two-point seismic source model with significant overlap for the White Wolf fault, which propagates upward(20 km to 5 km) from SW to NE, fits most of the observed seismic waveforms in the least squares sense. Comparison of P, T and B axes of focal mechanisms and focal depths suggests that seismic source characteristics of the Kern County earthquake is consistant with those of Korean Peninsula Seismotectonics.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.155-161
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• 2001

Anisotropic DWI - Mapping of the Proton Diffusion "tensor". In neural ordered tissue, it is thought that water diffusion is mainly influenced by the presence of myelin sheaths and intracellular structures. Perpendicular to the fiber tracts, the cholesterol-laden myelin lipid bilayers might restrict or hinder the spins from diffusing through the normally highly permeable cytomembrane. Diffusion along the fiber is more or less determined by subcellular structures, such as the endoplasmatic reticulum, mitochondria, neuro-filaments and macromolecules. In addition to that, the entire complex of axons and stabilizing tissue (i.e., glia cells, astrocytes) is also assumed to influence diffusion due to the tortuosity of proton translation, but the uniform distribution of such cells throughout the brain might render this notion less important as initially anticipated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.10C
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• pp.958-966
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• 2003

Change detection algorithms based on frame difference are frequently used for finding moving objects in image sequences. These algorithms detect the change of frames using estimated statistical background model. But, if this estimated background model is different from the actual statistical distribution, false detections are generated. In this paper, we propose an improved change detection algorithm using euler number and structure tensor. The proposed mapping method which is based on the euler number can be used for reducing the false detections that generated by nonparametric change detection algorithm. In this paper, the change in the region of moving object also can be detected by the proposed method using structure tensor. Experimental result shows that the proposed method reduces the false detections effectively by 90% on "Weather", by 34% on "Mother & daughter" and by 43% on "Aisle" than an existing method does.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.607-629
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• 2022

In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝⁿ, g₀) → (Nⁿ, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.429-436
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• 2003

A new linkage framework between elastic shell element with finite rotation and computar-aided geometric design (CAGD) (or surface is developed in the present study. The framework of shell finite element is based on the generalized curved two-parametric coordinate system. To represent free-form surface, cubic B-spline tensor-product functions are used. Thus the present finite element can be directly linked into the geometric modeling produced by surface generation tool in CAD software. The efficiency and accuracy of the Previously developed linear elements hold for the nonlinear element with finite rotations. To handle the finite rotation behavior of shells, exponential mapping in the SO(3) group is employed to allow the large incremental step size. The integrated frameworks of shell geometric design and nonlinear computational analysis can serve as an efficient tool in shape and topological design of surfaces with large deformations.