• Journal of Korea Water Resources Association
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• v.44 no.10
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• pp.831-841
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• 2011

In this study, with the assumption that the geographical characteristics of the river basin have selfsimilarity, fractal dimensions are used to quantify the complexity of the terrain. For this, Area exponent and hurst exponent was applied to estimate the fractal dimension by using spatial analysis. The result shows that the value of area exponent and hurst exponent calculated by the fractal dimension are 2.008~2.074 and 2.132~2.268 respectively. Also the $R^2$ of area exponent and hurst exponent are 94.9% and 87.1% respectively too. It shows that the $R^2$ is relatively high. After analyzing the spatial self-similarity parameter, it is shown that traditional urban area's moderate slope geographical characteristic closed to 2D fractal in Ara water way. In addition, the relation between fractal dimension and geographical elements are identified. With these results, fractal dimension is the representative value of basin characteristics.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.9 no.3
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• pp.115-124
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• 1997

We measured the variance of eddy diffusion and associated ‘diffusion coefficients’ in coastal regions of Korea by observing the separation distances among multiple drifters deployed simultaneously at the same initial position. The variance of eddy diffusion was found to be proportional to $t^m$, where t is the time and m is a non-integer scaling exponent between 1.5 and 3.5. The observed scaling exponent of eddy diffusion cannot be reproduced by diffusion models employing constant eddy diffusivity. In this study, we applied fractal theory in simulating exponential increase of variance of eddy diffusion. We employed the fGn(fractional Gaussian noise) as a ‘modified’ random walks corresponding to the oceanic eddy diffusion. The variance of eddy diffusion, which corresponds to the fBm(fractional Brown motion) of our diffusion model, is proportional to $t^{2H}$, where H is Hurst scaling exponent. The temporal increase of the variance. with scaling exponent between 1 and 2, was successfully reproduced by our fractal diffusion model. However, our model cannot reproduce scaling exponent greater than 2. The scaling exponents greater than 2 are associated with the velocity shear of the mean flow.

• The Korean Journal of Financial Management
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• v.24 no.3
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• pp.63-89
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• 2007

This study aims at empirically verifying whether long memory properties exist in returns and volatility of the financial time series and then, empirically observing influential factors of long-memory properties. The presence of long memory properties in the financial time series is examined with the Hurst exponent. The Hurst exponent is measured by DFA(detrended fluctuation analysis). The empirical results are summarized as follows. First, the presence of significant long memory properties is not identified in return time series. But, in volatility time series, as the Hurst exponent has the high value on average, a strong presence of long memory properties is observed. Then, according to the results empirically confirming influential factors of long memory properties, as the Hurst exponent measured with volatility of residual returns filtered by GARCH(1, 1) model reflecting properties of volatility clustering has the level of $H{\approx}0.5$ on average, long memory properties presented in the data before filtering are no longer observed. That is, we positively find out that the observed long memory properties are considerably due to volatility clustering effect.

• Journal of The Korean Society of Agricultural Engineers
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• v.47 no.7
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• pp.37-45
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• 2005

In this study, R/S analysis which was proposed by Mandelbrot & Wallis (1969) was applied to evaluate the presence of the fractal property in the cone tip resistance of in-situ CPT data. Hurst exponents (H) were evaluated in the range of 0.660$\sim$0.990 and the average was 0.875. It was confirmed that a cone tip resistance data had the characteristic of fractals and it was expected that cone tip resistance data sets are well approximated by a fBm process with an Hurst exponent near 0.875. It was also observed that the boundary between layers were obviously identified as a result of R/S analysis and it will be usage in practices.

• Journal of Korea Multimedia Society
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• v.24 no.12
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• pp.1614-1623
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• 2021

In this paper, the purpose is evaluation of the effect of using fractal feature in machine learning based pancreatic tumor classification. We used the data that Pancreas CT series 469 case including 1995 slice of benign and 1772 slice of malignant. Feature selection is implemented from 109 feature to 7 feature by Lasso regularization. In Fractal feature, fractal dimension is obtained by box-counting method, and hurst coefficient is calculated range data of pixel value in ROI. As a result, there were significant differences in both benign and malignancies tumor. Additionally, we compared the classification performance between model without fractal feature and model with fractal feature by using support vector machine. The train model with fractal feature showed statistically significant performance in comparison with train model without fractal feature.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.271-274
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• 1998

In this paper we examine long-term memory of the financial time-series by employing the R/S analysis, the Hurst exponent estimation, and the modified R/S analysis. The null hypothesis of white-noise is tested using the NYSE daily indexes from January 1966 to July 1998, and the results show that long-range dependence exists before the apparent structural break of the Black Monday in 1987.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.04a
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• pp.73-76
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• 2001

We have simulated the effect of fracture characteristics on reduction of effective permeability of the fractured rocks due to in-situ bacteria growth. A nutrient is injected continuously for growth of in-situ bacteria. We used a power law for fracture length distribution and a fBm for fracture aperture spatial distribution. The results show that in-situ bacteria growth reduces the Permeability hyperbolically, but the porosity of backbone fracture does not change significantly. It shows that reduction of the permeability proceeds at faster speed for smaller value of length exponent(a) and for larger value of Hurst exponent(H). The fracture length distribution has stronger effect on speed of reduction than the aperture spatial distribution. The time needed to reduce permeability is inversely proportional to the hydraulic gradient.

• Journal of Korea Water Resources Association
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• v.42 no.9
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• pp.691-702
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• 2009

This study makes a systematic approach to Hack's law considering self-affinity and self-similarity of natural basins as well as the elongation of corresponding catchment-plan forms. Catchment-plan forms extracted from DEM appear to be the population come from the interactions of 2 hypotheses on Hack's law. It is judged that the elongation measures based on inertia moments are more intuitive than the ones based on main channel lengths. The exponent of Hack's law, h, seems to be similar to the result of Gray's study (1961). However Hurst exponent, H, being 0.96 imply that catchment-plan forms considered in this study have isotropic increasing properties with scale. From this point of view it is inferred that the shapes of the basins in this study would be more affected from self-similarity of main channel lengths than self-affinity of catchment-plan forms.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.125-125
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• 2020

European Space Agency's Sentinel-1 has an improved spatial and temporal resolution, as compared to previous satellite data such as Envisat Advanced SAR (ASAR) or Advanced Scatterometer (ASCAT). Thus, the assumption used for low-resolution retrieval algorithms used by ENVISAT ASAR or ASCAT is not applicable to Sentinel-1, because a higher degree of land surface heterogeneity should be considered for retrieval. The assumption of homogeneity over land surface is not valid any more. In this study, considering that soil roughness is one of the key parameters sensitive to soil moisture retrievals, various approaches are discussed. First, soil roughness is spatially inverted from Sentinel-1 backscattering over Yanco sites in Australia. Based upon this, Artificial Neural Networks data (feedforward multiplayer perception, MLP, Levenberg-Marquadt algorithm) are compared with Fractal approach (brownian fractal, Hurst exponent of 0.5). When using ANNs, training data are achieved from theoretical forward scattering models, Integral Equation Model (IEM). and Sentinel-1 measurements. The network is trained by 20 neurons and one hidden layer, and one input layer. On the other hand, fractal surface roughness is generated by fitting 1D power spectrum model with roughness spectra. Fractal roughness profile is produced by a stochastic process describing probability between two points, and Hurst exponent, as well as rms heights (a standard deviation of surface height). Main interest of this study is to estimate a spatial variability of roughness without the need of local measurements. This non-local approach is significant, because we operationally have to be independent from local stations, due to its few spatial coverage at the global level. More fundamentally, SAR roughness is much different from local measurements, Remote sensing data are influenced by incidence angle, large scale topography, or a mixing regime of sensors, although probe deployed in the field indicate point data. Finally, demerit and merit of these approaches will be discussed.

• Journal of Information Technology Applications and Management
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• v.21 no.3
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• pp.1-17
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• 2014

In this study, various characteristics of R&D related economic variables were studied to analyze complexity of science and technology activities in Korea, as reliance of R&D activities of the private sector is growing by the day. In comparison to other countries, this means that it is likely to be fluctuated by economic conditions. This complexity characteristic signifies that the result of science and technology activities can be greatly different from the anticipated results - depending on the influences from economic conditions and the results of science and technology activities which may be unpredictable. After reviewing the results of 17 variables related to science and technology characteristics of complex systems intended for time-series data - in the total R&D expenditure, and private R&D expenditure, numbers of SCI papers, the existence of chaotic characteristics were. using Lyapunov Exponent, Hurst Exponent, BDS test. This result reveals science and technology activity of the three most important components in Korea which are; heavy dependence on initial condition, the long term memory of time series, and non-linear structure. As stable R&D investment and result are needed in order to maintain steady development of Korea economy, the R&D structure should be less influenced by business cycles and more effective technology development policy for improving human resource development must be set in motion. And to minimize the risk of new technology, the construction of sophisticated technology forecasting system should take into account, for development of R&D system.