• Honam Mathematical Journal
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• v.9 no.1
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• pp.113-119
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• 1987

Random variables $X_1$, $X_1$, ..., $X_m$ are said to be weakly associated if whenever $\pi$ is a permutation of {1, 2,..., m}, $1{\leq}k<m$, and f: $R^{k}{\rightarrow}R$, g: $R^{m-k}{\rightarrow}R$ are coordinatewise nondecreasing functions then Cov $[f(X_{x(1)},...,\;X_{\pi(k)},\;g(X_{x(k+1)},...,\;X_{x(m)})]{\geq}0$, whenever the covariance is defined. An infinite collection of random variables is weakly associated if every finite subcollection is weakly associated. The basic properties of weak association and central limit theorem for weakly associated random variables are derived. We also extend this idea to point random fields and prove that a Cox process with a stationary weakly associated intensity rardom measure is weakly associated. Another inequalities and the fact that positive correlated normal random variables are weakly associated are also proved.

• Journal of the Korean Chemical Society
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• v.38 no.3
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• pp.221-223
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• 1994

We tried to apply the linear solvation energy comparison method to solute retention in normal phase liquid chromatography. Correlation coefficients of regression of lnk' collected in a fixed eluent against solute polarity indices have proven to be lower than those obtained from reversed phase liquid chromatography data. This event can be attributed to complexity of solute retention process in normal phase liquid chromatography. We concluded from the regression results that each specific polarity of the stationary phase is greater than that of the mobile phase and that the difference in each polarity between the stationary phase and the mobile phase decreases as the volume fraction(${\phi}$) of the more polar solvent in the mobile phase increases. Correlations of lnk' of a single solute against solvent polarity indices have proven to be meaningless owing to covariance among the solvent polarity indices. Instead, a good linear relationship between lnk' and solvent ${\pi}^*$ was observed, and its linearity is better than that between lnk' and ${\phi}$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.8A
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• pp.741-747
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• 2011

Matrix Pencil method is one of the promising method to estimate DOA in non-stationary, multi-path coherent environment. Not only the Matrix Pencil Method offers better resolution than the conventional approach using covariance matrix, but also it is computationally very efficient. In this paper, we presented an effect of unbalanced data weighting in the formulation of the Matrix Pencil method. A new formulation has been suggested to mitigate the effect of unbalanced data weighting. Numerical simulation demonstrated that the proposed method can successfully eliminate the problem of unbalanced data weighting.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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• pp.415-421
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• 2009

TOA(time-of-arrival) and TDOA(time-difference-of-arrival) positioning techniques are commonly used in many radio-navigation systems. From the literature, it is known that the position estimate and error covariance matrix of TDOA obtained by GN(Gauss-Newton) method is exactly the same as that of TOA when the error source of the range measurement is only an IID white Gaussian noise. In case of geo-location and indoor positioning, however, multi-path or NLOS(non-line-of-sight) error is frequently appeared in range measurements. Though its occurrence is random, the multipath acts like a bias for a stationary user if it occurs. This paper presents the comparisons of error characteristics between TOA and TDOA positioning in presence of multi-path or NLOS error. It is analytically shown that the position estimate of TDOA is exactly the same as that of TOA even when bias errors are included in range measurements with different magnitudes. By computer simulation, position estimation error and error distribution are analyzed in presence of range bias errors.

• Korean Journal of Agricultural and Forest Meteorology
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• v.21 no.1
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• pp.29-41
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• 2019

Terrestrial Gross Primary Production (GPP) is the largest global carbon flux, and forest ecosystems are important because of the ability to store much more significant amounts of carbon than other terrestrial ecosystems. There have been several attempts to estimate GPP using mechanism-based models. However, mechanism-based models including biological, chemical, and physical processes are limited due to a lack of flexibility in predicting non-stationary ecological processes, which are caused by a local and global change. Instead mechanism-free methods are strongly recommended to estimate nonlinear dynamics that occur in nature like GPP. Therefore, we used the mechanism-free machine learning techniques to estimate the daily GPP. In this study, support vector machine (SVM), random forest (RF) and artificial neural network (ANN) were used and compared with the traditional multiple linear regression model (LM). MODIS products and meteorological parameters from eddy covariance data were employed to train the machine learning and LM models from 2006 to 2013. GPP prediction models were compared with daily GPP from eddy covariance measurement in a deciduous forest in South Korea in 2014 and 2015. Statistical analysis including correlation coefficient (R), root mean square error (RMSE) and mean squared error (MSE) were used to evaluate the performance of models. In general, the models from machine-learning algorithms (R = 0.85 - 0.93, MSE = 1.00 - 2.05, p < 0.001) showed better performance than linear regression model (R = 0.82 - 0.92, MSE = 1.24 - 2.45, p < 0.001). These results provide insight into high predictability and the possibility of expansion through the use of the mechanism-free machine-learning models and remote sensing for predicting non-stationary ecological processes such as seasonal GPP.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.5
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• pp.177-187
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• 2014

This paper proposes a fast subspace tracking methods, which is called GVFF FAPI, based on FAPI (Fast Approximated Power Iteration) method and GVFF RLS (Gradient-based Variable Forgetting Factor Recursive Lease Squares). Since the conventional FAPI uses a constant forgetting factor for estimating covariance matrix of source signals, it has difficulty in applying to non-stationary environments such as continuously changing DOAs of source signals. To overcome the drawback of conventioanl FAPI method, the GVFF FAPI uses the gradient-based variable forgetting factor derived from an improved means square error (MSE) analysis of RLS. In order to achieve the decreased subspace error in non-stationary environments, the GVFF-FAPI algorithm used an improved forgetting factor updating equation that can produce a fast decreasing forgetting factor when the gradient is positive and a slowly increasing forgetting factor when the gradient is negative. Our numerical simulations show that GVFF-FAPI algorithm offers lower subspace error and RMSE (Root Mean Square Error) of tracked DOAs of source signals than conventional FAPI based MUSIC (MUltiple SIgnal Classification).

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.323-332
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• 2007

We present a new type of portmanteau test in the frequency domain which is derived from the discrete cosine transform(DCT). For the stationary time series, DCT coefficients are asymptotically independent and their variances are expressed by linear combinations of autocovariances. The covariance matrix of DCT coefficients for white noises is diagonal matrix whose diagonal elements is the variance of time series. A simple way to test the independence of time series is that we divide DCT coefficients into two or three parts and then compare sample variances. We also do this by testing the slope in the linear regression model of which the response variables are absolute values or squares of coefficients. Simulation results show that the proposed tests has much higher powers than Ljung-Box test in most cases of our experiments.

• Korean Journal of Remote Sensing
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• v.35 no.6_2
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• pp.1117-1132
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• 2019

Forest covers 30% of the Earth's land area and plays an important role in global carbon flux through its ability to store much greater amounts of carbon than other terrestrial ecosystems. The Gross Primary Production (GPP) represents the productivity of forest ecosystems according to climate change and its effect on the phenology, health, and carbon cycle. In this study, we estimated the daily GPP for a forest ecosystem using remote-sensed data from Moderate Resolution Imaging Spectroradiometer (MODIS) and machine learning algorithms Support Vector Machine (SVM). MODIS products were employed to train the SVM model from 75% to 80% data of the total study period and validated using eddy covariance measurement (EC) data at the six flux tower sites. We also compare the GPP derived from EC and MODIS (MYD17). The MODIS products made use of two data sets: one for Processed MODIS that included calculated by combined products (e.g., Vapor Pressure Deficit), another one for Unprocessed MODIS that used MODIS products without any combined calculation. Statistical analyses, including Pearson correlation coefficient (R), mean squared error (MSE), and root mean square error (RMSE) were used to evaluate the outcomes of the model. In general, the SVM model trained by the Unprocessed MODIS (R = 0.77 - 0.94, p < 0.001) derived from the multi-sites outperformed those trained at a single-site (R = 0.75 - 0.95, p < 0.001). These results show better performance trained by the data including various events and suggest the possibility of using remote-sensed data without complex processes to estimate GPP such as non-stationary ecological processes.