• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.331-350
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• 2010

We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map. The proof is based on Young measures.

• Journal of Forest and Environmental Science
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• v.30 no.1
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• pp.71-75
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• 2014

Forest roads failure is one of the most common problems caused by heavy rainfalls. This study investigated the characteristics on stabilization measures installed for cutting slopes failure of forest road resulted from heavy rainfalls. Three primary factors (slope length, slope gradient, soil type) affecting cutting slope failure were considered and stabilization measures were classified into two types (A type: wooden fence, vegetation sandbag, stone masonry; B type: wire cylinder, gabion, concrete retaining wall) through discriminant analysis based on their capacity of resistance to slope failure. Results showed that A type was mainly installed in such conditions as cut slope <8 m, cut slope gradient $30-40^{\circ}$ and soil type with soil while B type occurred in locational conditions as cut slope length >8 m, cut slope gradient < $30^{\circ}$ and > $30^{\circ}$, and soil type of gravelly soil and rock.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.5 no.5
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• pp.22-29
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• 2002

This study was conducted to suggest develop revegetation methods and to classification of cutting-rock slopes revegetation type. The data was collected from pre-experienced data, reports and journal. Also research result was reflected from field research for the conditions of construction, vegetation types and field conditions. As the result of analyze, the factors affecting the plant coverage rates of cutting-rock slopes were period of construction, revegetation methods, slope gradient and slope length. Classification of cutting-rock slopes revegetation type was fourth from material of revegetation measures and spray type. It is recommended to adjust the proposed factor as environment, field condition and characteristic related with revegetation measures on slopes for the presentation of revegetation standard.

• Journal of Korean Society of Forest Science
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• v.86 no.4
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• pp.476-488
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• 1997

The purpose of this study was to figure out the suitable field standards for revegetation measures on cut-slopes in consideration of the environmental factors. The field survey was conducted from 1995 to 1996 on highway cut-slopes. The results obtained could be summarized as follows; The major revegetation measures surveyed were 5 major measures as a whole in descending order of seed-spraying measures, block-sod pitching measures, latticed block pitching measures, hydro-seeding measures with seed-fertilizer-soil materials, and several netting measures on highway cut-slopes. According to the analysis of the environmental factors, the plant coverage was affected several major environmental factors which were soil factors(soil hardness, soil texture, soil and rock condition), and site factors(slope gradient, slope length). From a viewpoint of optimum selection, the major 3 factors(soil factors, slope gradient factors, slope length factors) should be considered for selection of revegetation measures on highway cut-slopes.

• Journal of Biomedical Engineering Research
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• v.28 no.6
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• pp.817-824
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• 2007

Tractography using Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvector in the white matter of the brain. However, the fiber tracking methods suffer from the noise included in the diffusion tensor images that affects the determination of the principal eigenvector. As the fiber tracking progresses, the accumulated error creates a large deviation between the calculated fiber and the real fiber. This problem of the DT-MRI tractography is known mathematically as the ill-posed problem which means that tractography is very sensitive to perturbations by noise. To reduce the noise in DT-MRI measurements, a tensor-valued median filter which is reported to be denoising and structure-preserving in fiber tracking, is applied in the tractography. In this paper, we proposed the modified gradient descent method which converges fast and accurately to the optimal tensor-valued median filter by changing the step size. In addition, the performance of the modified gradient descent method is compared with others. We used the synthetic image which consists of 45 degree principal eigenvectors and the corticospinal tract. For the synthetic image, the proposed method achieved 4.66%, 16.66% and 15.08% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively. For the corticospinal tract, at iteration number ten the proposed method achieved 3.78%, 25.71 % and 11.54% less error than the conventional gradient descent method for error measures AE, AAE, AFA respectively.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1418-1421
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• 1987

An important problem in edge detection is to select a proper threshold that transforms the gradient picture to e two level picture containing optimum edges between regions, Such a threshold is determined depending on some measures of errors in tresholding. In this paper, an error criterion on extracting edges by thresholding the block gradient image is presented. Based on the error measure, the optimum threshold is chosen for the detection of acceptable edges.

• Journal of Environmental Impact Assessment
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• v.17 no.6
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• pp.357-366
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• 2008

It is certain that urbanization has transformed the ecological consequences severely, but urban ecosystem is not fully understood yet. Urban growth is not like a static form and it spreads spatially and temporally. Therefore in studying urban ecosystem, it is important to relate the spatial pattern of urbanization to ecological processes. Using gradient analysis, we attempted to quantify the urbanization's spatial impacts in Daejeon-city and Cheonan-city, Chungcheong-province, Korea. Because of Multifunctional Administrative City Planning (MACP), a lot of development projects are planned in Chungcheong-province, Korea. It's important to study about original cities' patterns and impacts. These results can be adopted to future city planning. So several measures such as fragmentation, vegetation index, surface temperature, population density, and income rate were computed along a 75km long and 3km wide transect. The results showed that Daejeon-city has a wider urban center, lower vegetation indexes, and higher surface temperature than Cheonan-city. Therefore in the perspective of urban environments and sustainable urbanism, it seems that Cheonan-city is better than Daejeon-city. The changes along the transect have important ecological implications, and quantifying the urbanization gradient is an important step in understanding urban ecology.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.7 no.2
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• pp.12-20
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• 2004

This study was carried out from January 1998 to December 1999 to report the revegetation of cutting-rock slopes and a design standard in the highway cut-slopes. The field data was collected from the 67 sites cutting-rock slopes of highways, local roads, and field test. As the result of analyze, cutting-rock slopes revegetation measures were 16 types. There were Vine planting(3 types), Hydroseeding measures with seed-fertilizer-soil materials(5 types), Vegetaion-base spraying measures(5 types), and Stability measures(3 types). The factors affecting the plant coverage rates of cutting-rock slopes were the slope gradient, the slope width and direction. The plant coverage rate decreases in the condition of steep slope and long slope width and length(height). In addition, the plant coverage rates of the westward and southward were lower than that of the northward and eastward. Most dominant species were Zoysia japonica, Lespedeza cyrtobotrya, Lespedeza cuneata, Rubus crataegifolius, Miscanthus sinensis, Arrundinella hirta, Themeda triandra, and Oenothera odorata. Exotic species were Eragrostis curvula(Weeping lovegrass), Dactylis glomerata Orchardgrass), Lolium perenne(Perennial ryegrass), and Festuca arundinacea(Tall fescue). It is recommended to adjust the proposed factor as environment, topsoil, classification of rock, field condition and characteristic related with revegetation measures on slopes for the presentation of revegetation standard.