• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1557-1566
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• 2006

We present a procedure for the application of global orthogonal polynomial into an atmospheric re-entry maneuvering problem. This trajectory optimization is imbedded in a family of canonically parameterized optimal control problem. The optimal control problem is transcribed to nonlinear programming via global orthogonal polynomial and is solved a sparse nonlinear optimization algorithm. We analyze the optimal trajectories with respect to the performance of re-entry maneuver.

• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.44-54
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• 2012

In wireless sensor networks, a moving object tracking scheme is one of core technologies for real applications such as environment monitering and enemy moving tracking in military areas. However, no works have been carried out on processing the failure of object tracking in sparse sensor networks with holes. Therefore, the energy consumption in the existing schemes significantly increases due to plenty of failures of moving object tracking. To overcome this problem, we propose a novel moving object tracking scheme based on polynomial regression prediction in sparse sensor networks. The proposed scheme activates the minimum sensor nodes by predicting the trajectory of an object based on polynomial regression analysis. Moreover, in the case of the failure of moving object tracking, it just activates only the boundary nodes of a hole for failure recovery. By doing so, the proposed scheme reduces the energy consumption and ensures the high accuracy for object tracking in the sensor network with holes. To show the superiority of our proposed scheme, we compare it with the existing scheme. Our experimental results show that our proposed scheme reduces about 47% energy consumption for object tracking over the existing scheme and achieves about 91% accuracy of object tracking even in sensor networks with holes.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.303-311
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• 2003

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts, et al.(2000) presented $T_1=\sum\limits_{i=1}^k(\hat{p}_i-p_i)^2$ as a test statistic with the local polynomial estimator $(\hat{p}_i$, and showed its asymptotic distribution. When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T=\sum\limits_{i=1}^k(\hat{p}_i-p_i)^2/p_i$ instead, and show it follows an asymptotic normal distribution.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.179-188
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• 1998

Local polynomial regression estimation is the most popular one among kernel type regression estimator. In local polynomial regression function esimation bandwidth selection is crucial problem like the kernel estimation. When the regression curve has complicated structure variable bandwidth selection will be appropriate. In this paper, we propose a variable bandwidth selection method fully data driven. We will choose the bandwdith by selecting minimising estiamted MSE which is estimated by the pilot bandwidth study via croos-validation method. Monte carlo simulation was conducted in order to show the superiority of proposed bandwidth selection method.

• The KIPS Transactions:PartD
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• v.10D no.7
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• pp.1145-1148
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• 2003

We show the mixed finite element method which induces solutions that has the same order of errors for both the gradient of the solution and the solution itself. The technique to construct an efficient reusable matrix is suggested. Two families of mixed finite element methods are introduced with an automatic generating technique for matrix with my order of basis. The generated matrix by this technique has more accurate values and is a sparse matrix. This new technique is applied to solve a minimal surface problem.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.86-89
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• 2003

To model a numerical problem space under the limitation of available data, we need to extract sparse but key points from the space and to efficiently approximate the space with them. This study proposes a sampling method based on the search process of genetic algorithm and a space modeling method based on least-squares approximation using the summation of Gaussian functions. We conducted simulations to evaluate them for several kinds of problem spaces: DeJong's, Schaffer's, and our original one. We then compared the performance between our sampling method and sampling at regular intervals and that between our modeling method and modeling using a polynomial. The results showed that the error between a problem space and its model was the smallest for the combination of our sampling and modeling methods for many problem spaces when the number of samples was considerably small.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.2
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• pp.211-222
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• 2023

Multivariate quadratic equations (MQ)-based public-key cryptographic algorithms are one of promising post-quantumreplacements for currently used public-key cryptography. After selecting to NIST Post-Quantum Cryptography StandardizationRound 3 as one of digital signature finalists, Rainbow was cryptanalyzed by advanced algebraic attacks due to its multiple layered structure. The researches on MQ-based schemes are focusing on UOV with a single layer. In this paper, we propose a new MQ-signature scheme based on UOV using the combinations of the special structure of linear equations, spare polynomials and random polynomials to reduce the secret key size. Our scheme uses the block inversion method using half-sized blockmatrices to improve signing performance. We then provide security analysis, suggest secure parameters at three security levels and investigate their key sizes and signature sizes. Our scheme has the shortest signature length among post-quantumsignature schemes based on other hard problems and its secret key size is reduced by up to 97% compared to UOV.