• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.6
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• pp.3166-3187
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• 2017

For "generic" multivariate public key cryptography (MPKC) systems, experts believe that the Unbalanced Oil-Vinegar (UOV) scheme is a feasible signature scheme with good efficiency and acceptable security. In this paper, we address two problems that are to find inversion solution of quadratic multivariate equations and find another structure with some random Oil-Oil terms for UOV, then propose a novel signature scheme based on hyper-sphere (HS-Sign for short) which directly answers these two problems. HS-Sign is characterized by its adding Oil-Oil terms and more advantages compared to UOV. On the one side, HS-Sign is based on a new inversion algorithm from hyper-sphere over finite field, and is shown to be a more secure UOV-like scheme. More precisely, according to the security analysis, HS-Sign achieves higher security level, so that it has larger security parameters choice ranges. On the other side, HS-Sign is beneficial from both the key side and computing complexity under the same security level compared to many baseline schemes. To further support our view, we have implemented 5 different attack experiments for the security analysis and we make comparison of our new scheme and the baseline schemes with simulation programs so as to show the efficiencies. The results show that HS-Sign has exponential attack complexity and HS-Sign is competitive with other signature schemes in terms of the length of the message, length of the signature, size of the public key, size of the secret key, signing time and verification time.

• Wind and Structures
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• v.9 no.3
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• pp.231-243
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• 2006

An improvement to the spectral representation algorithm for the simulation of wind velocity fields on large scale structures is proposed in this paper. The method proposed by Deodatis (1996) serves as the basis of the improved algorithm. Firstly, an interpolation approximation is introduced to simplify the computation of the lower triangular matrix with the Cholesky decomposition of the cross-spectral density (CSD) matrix, since each element of the triangular matrix varies continuously with the wind spectra frequency. Fast Fourier Transform (FFT) technique is used to further enhance the efficiency of computation. Secondly, as an alternative spectral representation, the vectors of the triangular matrix in the Deodatis formula are replaced using an appropriate number of eigenvectors with the spectral decomposition of the CSD matrix. Lastly, a turbulent wind velocity field through a vertical plane on a long-span bridge (span-wise) is simulated to illustrate the proposed schemes. It is noted that the proposed schemes require less computer memory and are more efficiently simulated than that obtained using the existing traditional method. Furthermore, the reliability of the interpolation approximation in the simulation of wind velocity field is confirmed.

• Genomics & Informatics
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• v.20 no.1
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• pp.8.1-8.14
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• 2022

Despite the success of recent genome-wide association studies investigating longitudinal traits, a large fraction of overall heritability remains unexplained. This suggests that some of the missing heritability may be accounted for by gene-gene and gene-time/environment interactions. In this paper, we develop a Bayesian variable selection method for longitudinal genetic data based on mixed models. The method jointly models the main effects and interactions of all candidate genetic variants and non-genetic factors and has higher statistical power than previous approaches. To account for the within-subject dependence structure, we propose a grid-based approach that models only one fixed-dimensional covariance matrix, which is thus applicable to data where subjects have different numbers of time points. We provide the theoretical basis of our Bayesian method and then illustrate its performance using data from the 1000 Genome Project with various simulation settings. Several simulation studies show that our multivariate method increases the statistical power compared to the corresponding univariate method and can detect gene-time/ environment interactions well. We further evaluate our method with different numbers of individuals, variants, and causal variants, as well as different trait-heritability, and conclude that our method performs reasonably well with various simulation settings.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.421-421
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• 2017

In order to secure the safety of coastal areas from the continuous storm surge in Korea, it is important to predict the wave movement and properties accurately during the storm event. To improve the accuracy of the storm simulation, and to quantify coastal risks from the storm event, the dependencies between wave height, wave period, and storm duration should be analyzed. In this study, therefore, copulas were used to develop multivariate statistical models of sea storms. A case study of the east coast of Korea was conducted, and the dependencies between wave height, wave period, water level, storm duration and storm interarrival time were investigated using Kendall's tau correlation coefficient. As a result of the study, only wave height, wave period, and storm duration appeared to be correlated.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.655-667
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• 2018

To evaluate the stability of a rock slope with one pre-exiting vertical crack, this paper performs corresponding probabilistic stability analysis. The existence of cracks is generally ignored in traditional deterministic stability analysis. However, they are widely found in either cohesive soil or rock slopes. The influence of one pre-exiting vertical crack on a rock slope is considered in this study. The safety factor, which is usually adopted to quantity the stability of slopes, is derived through the deterministic computation based on the strength reduction technique. The generalized Hoek-Brown (HB) failure criterion is adopted to characterize the failure of rock masses. Considering high nonlinearity of the limit state function as using nonlinear HB criterion, the multivariate adaptive regression splines (MARS) is used to accurately approximate the implicit limit state function of a rock slope. Then the MARS is integrated with Monte Carlo simulation to implement reliability analysis, and the influences of distribution types, level of uncertainty, and constants on the probability density functions and failure probability are discussed. It is found that distribution types of random variables have little influence on reliability results. The reliability results are affected by a combination of the uncertainty level and the constants. Finally, a reliability-based design figure is provided to evaluate the safety factor of a slope required for a target failure probability.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.3
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• pp.40-45
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• 2018

Intelligent monitoring and diagnosis of production processes based on multivariate statistical methods has been one of important tasks for safety and quality issues. This is due to the fact that faults and unexpected events may have serious impacts on the operation of processes. This study proposes a diagnostic scheme based on effective representation of process measurement data and is evaluated using simulation process data. The effects of utilizing a preprocessing step and nonlinear statistical methods are also tested using fifteen faults of the simulation process. Results show that the proposed scheme produced more reliable results and outperformed other tested schemes with none of the filtering step and nonlinear methods. The proposed scheme is expected to be robust to process noises and easy to develop due to the lack of required rigorous mathematical process models or expert knowledge.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.1013-1024
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• 2015

We compare the performance of two representative estimation methods for the dynamic conditional correlation (DCC) GARCH model. The first method is the pairwise estimation which exploits partial information from the paired series, irrespective to the time series dimension. The second is the multi-dimensional estimation that uses full information of the time series. As a simulation for the comparison, we generate a multivariate time series similar to those observed in real markets and construct a DCC GARCH model. As an empirical example, we constitute various portfolios using real KOSPI 200 sector indices and estimate volatility and VaR of the portfolios. Through the estimated dynamic correlations from the simulation and the estimated volatility and value at risk (VaR) of the portfolios, we evaluate the performance of the estimations. We observe that the multi-dimensional estimation tends to be superior to pairwise estimation; in addition, relatively-uncorrelated series can improve the performance of the multi-dimensional estimation.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.540-544
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• 2009

Hydrologic pattern under climate change has been paid attention to as one of the most important issues in hydrologic science group. Rainfall and runoff is a key element in the Earth's hydrological cycle, and associated with many different aspects such as water supply, flood prevention and river restoration. In this regard, a main objective of this study is to evaluate design flood using simulation techniques which can consider a full spectrum of uncertainty. Here we utilize a weather state based stochastic multivariate model as conditional probability model for simulating the rainfall field. A major premise of this study is that large scale climatic patterns are a major driver of such persistent year to year changes in rainfall probabilities. Uncertainty analysis in estimating design flood is inevitably needed to examine reliability for the estimated results. With regard to this point, this study applies a Bayesian Markov Chain Monte Carlo scheme to the NWS-PC rainfall-runoff model that has been widely used, and a case study is performed in Soyang Dam watershed in Korea. A comprehensive discussion on design flood under climate change is provided.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.99-113
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• 2005

In this article, we propose a chi-squared test of spherical symmetry. The advantage of this test is that the test statistic and its asymptotic p-value are easy to compute. The limiting distribution of the test statistic is derived under spherical symmetry and its accuracy, in finite samples, is studied via simulation. Also, a simulation study is conducted in which the power of our test is compared with those of other tests for spherical symmetry in various alternative distributions. Finally, an illustrative example of application to a real data is provided.