• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.791-797
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• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• Quantitative Bio-Science
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• v.37 no.2
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• pp.133-141
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• 2018

Graphical lasso is one of the most popular methods to estimate a sparse precision matrix, which is an inverse of a covariance matrix. The objective function of graphical lasso imposes an ${\ell}_1$-penalty on the (vectorized) precision matrix, where a tuning parameter controls the strength of the penalization. The selection of the tuning parameter is practically and theoretically important since the performance of the estimation depends on an appropriate choice of tuning parameter. While information criteria (e.g. AIC, BIC, or extended BIC) have been widely used, they require an asymptotically unbiased estimator to select optimal tuning parameter. Thus, the biasedness of the ${\ell}_1$-regularized estimate in the graphical lasso may lead to a suboptimal tuning. In this paper, we propose a two-staged bias-correction procedure for the graphical lasso, where the first stage runs the usual graphical lasso and the second stage reruns the procedure with an additional constraint that zero estimates at the first stage remain zero. Our simulation and real data example show that the proposed bias correction improved on both edge recovery and estimation error compared to the single-staged graphical lasso.

• Geophysics and Geophysical Exploration
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• v.11 no.4
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• pp.326-334
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• 2008

The resistivity method has been used to image the electrical properties of the subsurface. Especially, this method has become suitable for monitoring since data could be rapidly and automatically acquired. In this study, we developed a time-lapse inversion algorithm for the interpretation of resistivity monitoring data. The developed inversion algorithm imposes a big penalty on the model parameter with small change, while a minimal penalty on the model parameter with large change compared to the reference model. Through the numerical experiments, we can ensure that the time-lapse inversion result shows more accurate and focused image where model parameters have changed. Also, applying the timelapse inversion method to the leakage detection of an embankment dam, we can confirm that there are three major leakage zones, but they have not changed over time.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.7
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• pp.1157-1166
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• 2001

In this paper, we investigated the degree of compensation for optical pulse shape distortion due to both chromatic dispersion and SPM(self phase modulation) in high speed optical transmission system with dispersion shift fiber. We adopted the power symmetric MSSI(mid-span spectral inversion) as compensation method. We used EOP(eye-opening penalty) parameter in order to evaluate the compensation efficiency of distorted optical pulse. We evaluated input signal power range being able to maintain stable reception performance in the case of various chirp parameter of modulated optical pulse. And, in order to verify the applicable to wideband WDM system, we evaluated the wavelength range being able to maintain stable reception performance through the EOP calculation of various dispersion coefficient of first fiber D$\_$11/. We showed that proposed MSSI is effective compensation method to down chirped optical pulse transmission rather than up chirped optical pulse transmission in anomalous dispersion range. And we showed that this method have possibility of relative high power transmission and wideband transmission in WDM system.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.29-42
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• 2006

This paper describes the design scheme of the three-dimensional structures based on the concept of the cellular automata simulation. The cellular automata simulation is performed according to the local rule. In this paper, the local rule is derived in the mathematical formulation from the optimization problem. The cell density is taken as the design variable. Two objective functions are defined for reducing the total weight of the structure and obtaining the fully stressed structure. The constraint condition is defined for defining the local rule. The penalty function is defined from the objective functions and the constraint condition. Minimization of the penalty function with respect to the design parameter leads to the local rule. The derived rule is applied to the design of the three-dimensional structure first. The final structure can be obtained successfully. However, the computational cost is expensive. So, in order to reduce the computational cost, the material parameters $c_1$ and $c_2$ and the value of the cell rejection criterion (CRC) are changed. The results show that the computational cost depends on the parameters and the CRC value.

• JSTS:Journal of Semiconductor Technology and Science
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• v.15 no.5
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• pp.437-444
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• 2015

In simulation-based circuit optimization, many simulation runs may be wasted while evaluating infeasible designs, i.e. the designs that do not meet the constraints. To avoid such a waste, this paper investigates the use of support vector machine (SVM) classifiers in predicting the design's feasibility prior to simulation and the optimal selection of the SVM parameters, namely, the Gaussian kernel shape parameter ${\gamma}$ and the misclassification penalty parameter C. These parameters affect the complexity as well as the accuracy of the model that SVM represents. For instance, the higher ${\gamma}$ is good for detailed modeling and the higher C is good for rejecting noise in the training set. However, our empirical study shows that a low ${\gamma}$ value is preferable due to the high spatial correlation among the circuit design candidates while C has negligible impacts due to the smooth and clean constraint boundaries of most circuit designs. The experimental results with an LC-tank oscillator example show that an optimal selection of these parameters can improve the prediction accuracy from 80 to 98% and model complexity by $10{\times}$.

• Nuclear Engineering and Technology
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• v.55 no.11
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• pp.4102-4111
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• 2023

In order to better perform thermal hydraulic calculation and analysis of supercritical water reactor, based on the experimental data of supercritical water, the model training and predictive analysis of the heat transfer coefficient of supercritical water were carried out by using the support vector machine (SVM) algorithm. The changes in the prediction accuracy of the supercritical water heat transfer coefficient are analyzed by the changes of the regularization penalty parameter C, the slack variable epsilon and the Gaussian kernel function parameter gamma. The predicted value of the SVM model obtained after parameter optimization and the actual experimental test data are analyzed for data verification. The research results show that: the normalization of the data has a great influence on the prediction results. The slack variable has a relatively small influence on the accuracy change range of the predicted heat transfer coefficient. The change of gamma has the greatest impact on the accuracy of the heat transfer coefficient. Compared with the calculation results of traditional empirical formula methods, the trained algorithm model using SVM has smaller average error and standard deviations. Using the SVM trained algorithm model, the heat transfer coefficient of supercritical water can be effectively predicted and analyzed.

• Geophysics and Geophysical Exploration
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• v.16 no.3
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• pp.131-138
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• 2013

We developed a method for inverting magnetic data to image 2D susceptibility models. The major difficulty in the inversion of the potential data is the nonuniqueness. Furthermore, generally the number of inversion blocks are greater than the number of the magnetic data available, and thus the magnetic inversion leads to under-determined problem, which aggravates the nonuniqueness. When the magnetic data were inverted by the general least-squares method, the anomalous susceptibility would be concentrated near the surface in the inverted section. To overcome this nonuniqueness problem, we propose a new resolution model constraint that is calculated from the parameter resolution. The model constraint imposes large penalty on the model parameter with good resolution, on the other hand small penalty on the model parameter with poor resolution. Thus, the deep-seated model parameter, generally having poor resolution, can be effectively resolved. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and is tested on real airborne data obtained at the Okcheon belt of Korea.

• Geophysics and Geophysical Exploration
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• v.16 no.3
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• pp.119-130
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• 2013

We developed a method for inverting magnetic data to recover the 3D susceptibility models. The major difficulty in the inversion of the potential data is the non-uniqueness and the vast computing time. The insufficient number of data compared with that of inversion blocks intensifies the non-uniqueness problem. Furthermore, there is poor depth resolution inherent in magnetic data. To overcome this non-uniqueness problem, we propose a resolution model constraint that imposes large penalty on the model parameter with good resolution; on the other hand, small penalty on the model parameter with poor resolution. Using this model constraint, the model parameter with a poor resolution can be effectively resolved. Moreover, the wavelet transform and parallel solving were introduced to save the computing time. Through the wavelet transform, a large system matrix was transformed to a sparse matrix and solved by a parallel linear equation solver. This procedure is able to enormously save the computing time for the 3D inversion of magnetic data. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and real airborne data obtained at the Geumsan area of Korea.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.321-325
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• 2004

Linear motor feed drive systems have been broadly used in machine tools or precision automatic feed systems. Recently, modem machine tools require high speed and high precision feed drive system to achieve high productivity. Unfortunately, a feed drive system, even though it was optimum designed, may experience severe transient vibrations during high-speed operation if its feed rate control is unsuitable. A rough feed rate curve having discontinuity in its acceleration profile causes a serious vibration problem in the feed slides system. This paper presents a feed rate optimization of a machine tool feed slide system, which is driven by a linear motor, for its minimum vibrations. Firstly, a 4-degree-of-freedom lumped parameter model is proposed for the vibration analysis of a linear motor driven machine tool feed drive system. Next, a feed rate optimization of the feed slide is carried out for minimum vibrations. The feed rate curve optimization strategy is to find out the most appropriate acceleration profile with jerk continuity. Of course, the optimized feed rate should approximate to the desired one as possible. A genetic algorithm with variable penalty function was used in this feed rate optimization.