• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.857-860
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• 1993

In this paper, we apply the self generating neuro fuzzy model (SGNFM) to the dimension analysis of the chaotic time series. Firstly, we formulate a nonlinear time series identification problem with nonlinear autoregressive (NARMAX) model. Secondly, we propose an identification algorithm using SGNFM. We apply this method to the estimation of embedding dimension for chaotic time series, since the embedding dimension plays an essential role for the identification and the prediction of chaotic time series. In this estimation method, identification problems with gradually increasing embedding dimension are solved, and the identified result is used for computing correlation coefficients between the predicted time series and the observed one. We apply this method to the dimension estimation of a chaotic pulsation in a finger's capillary vessels.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.2
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• pp.169-176
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• 2000

This paper is considered with the problem of embedding complete binary trees into 3-dimensional meshes using dimension-ordered routing with primary concern of minimizing link congestion. The authors showed that a complete binary tree with $2^P-1$ nodes can be embedded into a 3-dimensional mesh with optimum size, $2^P$ nodes, if the link congestion is two[14], (More precisely, the link congestion of each dimension is two, two, and one if the dimension-ordered routing is used, and two, one, and one if the dimension-ordered routing is not imposed.) In this paper, we present a scheme to find an embedding of a complete binary tree into a 3-dimensional mesh of size no larger than 1.27 times the optimum with link congestion one while using dimension-ordered routing.

• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.37-47
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• 2000

The method of delays is widely used for reconstruction chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau}_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau}_w$ instead. Unfortunately, ${\tau}_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau}_w$ has yet emerged. However, a new technique, called the C-C method, can be used to estimate either ${\tau}_d\;or\;{\tau}_w$. Using this method, we show that, for small data sets, fixing ${\tau}_w$, rather than ${\tau}_d$, does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m in increased.

• Proceedings of the Korea Water Resources Association Conference
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• 2000.05a
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• pp.37-47
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• 2000

The method of delays is widely used fur reconstructing chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau}_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau}_w$ instead. Unfortunately, ${\tau}_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau}_w$has yet emerged. However, a new technique, called the C-C method, can be used to estimate either ${\tau}_d{\;}or{\;}{\tau}_w$. Using this method, we show that, for small data sets, fixing ${\tau}_w$, rather than ${\tau}_d$, does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m is increased.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.205-214
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• 2016

Any open Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we will prove that, given any open Riemann surface, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. This result along with [5] now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension ${\geq}3$.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.282-282
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• 2000

The analysis of the radiation effect on matter has been performed using stochastic methods. Recently, It was discovered that the detector pulses of radiation can be analysed using deterministic method that utilizes the chaotic behaviour with an attractor found in a noise region. We acquired a time series for pulse tram of Am-241 using scintillation detector and reconstructed a phase space, then performed new analysis for the radiation detection signal by applying embedding theory, Lyapunov exponent, correlation dimension, autocorrelation dimension, and power spectrum.

• Ocean and Polar Research
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• v.28 no.4
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• pp.459-465
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• 2006

Ambient noise as a background noise in the ocean has been well known for its the various and irregular signal characteristics. Generally, these signals we treated as noise and they are analyzed through stochastical level if they don't include definite sinusoidal signals. This study is to see how ocean ambient noise can be analyzed by the chaotic analysis technique. The chaotic analysis is carried out with underwater ambient noise obtained in areas near the Korean Peninsula. The calculated physical parameters of time series signal are as follows: histogram, self-correlation coefficient, delay time, frequency spectrum, sonogram, return map, embedding dimension, correlation dimension, Lyapunov exponent, etc. We investigate the chaotic pattern of noises from these parameters. From the embedding dimensions of underwater noises, the assesment of underwater noise by chaotic analysis shows similar results if they don't include a definite sinusoidal signal. However, the values of Lyapunov exponent (divergence exponent) are smaller than that of random noise signal. As a result we confirm the possibility of classification of underwater noise using Lyapunov analysis.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.6
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• pp.390-395
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• 2005

Sunspots are dark areas that grow and decay on the lowest level of the sun that is visible from the Earth. Shot-term predictions of solar activity are essential to help plan missions and to design satellites that will survive for their useful lifetimes. This paper presents a parallel-structure fuzzy system(PSFS) for prediction of sunspot number time series. The PSFS consists of a multiple number of component fuzzy systems connected in parallel. Each component fuzzy system in the PSFS predicts future data independently based on its past time series data with different embedding dimension and time delay. An embedding dimension determines the number of inputs of each component fuzzy system and a time delay decides the interval of inputs of the time series. According to the embedding dimension and the time delay, the component fuzzy system takes various input-output pairs. The PSFS determines the final predicted value as an average of all the outputs of the component fuzzy systems in order to reduce error accumulation effect.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.