• Journal of Institute of Control, Robotics and Systems
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• v.20 no.4
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• pp.449-455
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• 2014

This paper presents a method for developing a TM (Traversability Map) from a DTM (Digital Terrain Model) collected by remote sensors of autonomous mobile robots. Such a map can be used to plan traversable paths and estimate navigation speed quantitatively in real time for robots capable of performing autonomous tasks over rough terrain environments. The proposed method consists of three parts: a DTM partition module which divides the DTM into equally spaced patches, a terrain information module which extracts the slope and roughness of the partitioned patches using the curve fitting and the fractal-based triangular prism method, and a traversability analysis module which assesses traversability incorporating with extracted terrain information and fuzzy inference to construct a TM. The potential of the proposed method is validated via simulation works over a set of fractal DTMs.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.897-899
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• 1997

The analysis of distribution line faults is essential to the proper protections of the power system. A high impedance fault does not make enough current to cause conventional protective devices. It is well known that undesirable operating conditions and certain types of faults on electric distribution feeders cannot be detected by using conventional protection system. This paper describes an algorithm using back-propagation neural network for pattern recognition and detection of high impedance faults. Fractal dimensions are estimated for distinction between random noise and chaotic behavior in the power system. The fractal dimension of the line current is also used as a indication of the high impedance fault.

• East Asian mathematical journal
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• v.25 no.3
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• pp.229-245
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• 2009

G. Cantor gave a deep influence to the society of mathematics in many ways, especially in the set theory. It is important for gifted and talented high school students in mathematics to understand the Euler constant and the fractal dimension of the Cantor set in a heuristic sense. On the historic basis of mathematics and the standard of high school students, we give the teaching method for the talented high school student to understand them better. Further we introduce the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs distribution and its first moment. We hope that from these topics, the gifted and talented students in mathematics will have insight in the analysis of mathematics.

• Journal of Information Processing Systems
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• v.20 no.3
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• pp.409-417
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• 2024

Excellent apparel design can increase market competitiveness. This article briefly introduced the theory of fractals and its application in the field of apparel design. The convolutional neural network (CNN) algorithm was used to assist in the evaluation of apparel designs. In the case analysis, the accuracy of the evaluation was validated by comparing the CNN algorithm with two other intelligent algorithms, support vector machine (SVM) and back propagation (BP). The evaluation of the proposed design showed that compared with SVM and BP algorithms, the CNN algorithm had higher accuracy in evaluating apparel designs. The evaluation result of the proposed apparel design not only further verifies the effectiveness of the CNN algorithm, but also demonstrates that the theory of fractals can be effectively applied in apparel design to provide more innovative designs.

• Journal of the Mineralogical Society of Korea
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• v.23 no.4
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• pp.367-375
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• 2010

Understanding the interactions between earth materials and fluids is essential for studying the diverse geological processes in the Earth's surface and interior. In order to better understand the interactions between earth materials and fluids, we explore the effect of specific surface area and porosity on structural parameters of pore structures. We obtained 3D pore structures, using random packing simulations of porous media composed of single sized spheres with varying the particle size and porosity, and then we analyzed configurational entropy for 2D cross sections of porous media and cube counting fractal dimension for 3D porous networks. The results of the configurational entropy analysis show that the entropy length decreases from 0.8 to 0.2 with increasing specific surface area from 2.4 to $8.3mm^2/mm^3$, and the maximum configurational entropy increases from 0.94 to 0.99 with increasing porosity from 0.33 to 0.46. On the basis of the strong correlation between the liquid volume fraction (i.e., porosity) and configurational entropy, we suggest that elastic properties and viscosity of mantle melts can be expressed using configurational entropy. The results of the cube counting fractal dimension analysis show that cube counting fractal dimension increases with increasing porosity at constant specific surface area, and increases from 2.65 to 2.98 with increasing specific surface area from 2.4 to $8.3mm^2/mm^3$. On the basis of the strong correlation among cube counting fractal dimension, specific surface area, and porosity, we suggest that seismic wave attenuation and structural disorder in fluid-rock-melt composites can be described using cube counting fractal dimension.

• The Korean Journal of Financial Management
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• v.21 no.1
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• pp.149-181
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• 2004

In this study we perform empirical tests using KOSPI return to investigate the existence of nonlinear characteristics in the generating process of stock returns. There are three categories in empirical tests; the test of nonlinear dependence, nonlinear stochastic process and nonlinear deterministic chaos. According to the analysis of nonlinearity, stock returns are not normally distributed but leptokurtic, and appear to have nonlinear dependence. And it's decided that the nonlinear structure of stock returns can not be completely explained using nonlinear stochastic models of ARCH-type. Nonlinear deterministic chaos system is the feedback system, which the past incidents influence the present, and it is the fractal structure with self-similarity and has the sensitive dependence on initial conditions. To summarize the results of chaos analysis for KOSPI return, it is the persistent time series, which is not IID and has long memory, takes biased random walk, and is estimated to be fractal distribution. Also correlation dimension, as the approximation of fractal dimension, converged stably within 3 and 4, and maximum Lyapunov exponent has positive value. This suggests that chaotic attractor and the sensitive dependence on initial conditions exist in stock returns. These results fit into the characteristics of chaos system. Therefore it's decided that the generating process of stock returns has nonlinear deterministic structure and follow chaotic process.

• Journal of the Korean Association of Geographic Information Studies
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• v.19 no.3
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• pp.127-143
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• 2016

This study explored the variability in the accuracy of dasymetric population estimation with different grid cell sizes. Dasymetric population maps for Fulton County, Georgia in the US were generated from 30m to 420m at intervals of 30m using an automated intelligent dasymetric mapping technique, population data, and original and simulated land use and cover data. The accuracies of dasymetric population maps were evaluated using RMSE and adjusted RMSE statistics. Lumped fractal dimension values were calculated for the dasymetric population maps generated from resolutions of 30m to 420m using the triangular prism surface area (TPSA) method. The results show that a grid cell size of 210m or smaller is required to estimate population more accurately in terms of thematic accuracy, but a grid cell size of 30m is required to meet an acceptable spatial accuracy of dasymetric population estimation in the study area. The fractal analysis also indicates that a grid cell size of 120m is the optimal resolution for dasymetric population estimation in the study area.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.9
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• pp.1151-1162
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• 1999

The effects of radial heat and $H_2O$ diffusion on the evolution of silica particles in coflow diffusion flames have been studied experimentally. The evolution of silica aggregate particles in coflow diffusion flames has been measured experimentally using light scattering and thermophoretic sampling techniques. The measurements of scattering cross section from $90^{\circ}$ light scattering have been utilized to calculate the aggregate number density and volume fraction using with combination of measuring the particle size and morphology through the localized sampling and a TEM image analysis. Aggregate or particle number densities and volume fractions were calculated using Rayleigh-Debye-Gans and Mie theory for fractal aggregates and spherical particles, respectively. Flame temperatures and volumetric differential scattering cross sections have been measured for different flame conditions such as inert gas species, $H_2$ flow rates, and burner injection configurations to examine the relation between the formation of particles and radial $H_2O$ diffusion. The comparisons of oxidation and flame hydrolysis have also been made for various $H_2$ flow rates using $N_2$ or $O_2$ as a carrier gas. Results indicate that the role of oxidation becomes dominant as both carrier gas($O_2$) and $H_2$ flow rates increases since the radial heat diffusion precedes $H_2O$ diffusion in coflow flames used in this study. The effect of carrier gas flow rates on the evolution of silica particles have also been studied. When using $N_2$ as a carrier gas, the particle volume fraction has a maximum at a certain carrier gas flow rate and as the flow rate is further increased, the hydrolysis reaction Is delayed and the spherical particles finally evolves into fractal aggregates due to decreased flame temperature and residence time.

• Journal of Biomedical Engineering Research
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• v.33 no.3
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• pp.141-147
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• 2012

In this paper, we have investigated effects of two specific meditations (Chinese qigong meditation and Kundalini yoga meditation) on the heart rate variability (HRV), which is a well-known quantitative measure of autonomic balance, of skilled students. To analyze the effects, the MIT/BIH physionet database was utilized. The database includes RR intervals of eight skilled Chinese qigong meditators (5 women and 3 men; age range 26-35) and four skilled Kundalini yoga meditators (2 women and 2 men; age range 20-52). RR intervals of each subject were measured before and during the meditations. For HRV analysis, we have used typical four HRV parameters - the low frequency to high frequency power ratio (LF/HF ratio), SD2/SD1 ratio, sample entropy, and fractal dimension. The LF/HF ratio was calculated by the autoregressive spectrum and the SD2/SD1 ratio was derived from the Poincar$\grave{e}$ plot. The sample entropy was computed from the phase space plot and the fractal dimension was estimated by the Higuchi's algorithm. In the experiments, the Wilcoxon signed rank test was employed because we used small datasets and compared HRV parameters before and during the meditations. As a result, we have found increment of the LF/HF and SD2/SD1 ratios in both meditations; whereas the sample entropy is decreased during the meditations. In addition, the fractal dimension is increased during the Chinese qigong meditation; whereas it is decreased during the Kundalini yoga meditation. The results show that the sympathetic nervous system is generally more activated in skilled Chinese qigong and Kundalini yoga meditators, but the activation of the parasympathetic nervous tone is suppressed.

• Imaging Science in Dentistry
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• v.42 no.1
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• pp.5-12
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• 2012

Purpose : This study was performed to evaluate possible variations in maxillary and mandibular bone texture of normal population using the fractal analysis, particles count, and area fraction in intraoral radiographs. Materials and Methods : Periapical radiographs of patients who had full mouth intraoral radiographs were collected. Regions of interest ($100{\times}100$ pixels) were located between the teeth of the maxillary anterior, premolar, and molar area, as well as the mandibular anterior, premolar, and molar areas. The fractal dimension (FD) was calculated by using the box counting method. The particle count (PC) and area fraction (AF) analyses were also performed. Results : There was no significant difference in the FD values among the different groups of age, gender, upper, and lower jaws. The mean FD value was $1.49{\pm}0.01$. The mean PC ranged from 44 to 54, and the mean AF ranged from 10.92 to 11.85. The values of FD, PC, and AF were significantly correlated with each other except for the upper molar area. Conclusion : According to the results, patients with normal trabecular pattern showed a FD of approximately 1.5. Based on these results, further investigation would be recommended if the FD value of patient significantly differenct from this number, since the alteration of this value indicates microstructural modification of trabecular pattern of the jaws. Additionally, with periapical radiographs, simple and cost-effective, PC and AF could be used to assess the deviation from the normal.