• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.10
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• pp.2497-2513
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• 2013

In 2010, Dijk et al. demonstrated a simple somewhat homomorphic encryption (HE) scheme over the integers of which this simplicity came at the cost of a public key size in $\tilde{O}({\lambda}^{10})$. Although in 2011 Coron et al. reduced the public key size to $\tilde{O}({\lambda}^7)$, it is still too large for practical applications, especially for the cloud computing. In this paper, we propose a new form of somewhat HE scheme to reduce further the public key size and a variation of the scheme to optimize the ciphertext size. First of all, we propose a new somewhat HE scheme which is built on the hardness of the approximate greatest common divisor (GCD) problem of two integers, where the public key size in the scheme is reduced to $\tilde{O}({\lambda}^3)$. Furthermore, we can reduce the length of the ciphertext of the new somewhat HE scheme by applying the modular reduction technique. Additionally, we give simulation results for evaluating ability of the proposed scheme.

• Atmosphere
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• v.17 no.1
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• pp.17-26
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• 2007

The station relocations, the replacement of instruments, and the change of a procedure for calculating derived climatic quantities from observations are well-known nonclimatic factors that seriously contaminate the worthwhile results in climate study. Prior to embarking on the climatological analysis, therefore, the quality and homogeneity of the utilized data sets should be properly evaluated with metadata. According to the metadata of the Korea Meteorological Administration (KMA), there have been plenty of changes in the procedure computing the daily mean values of temperature, humidity, etc, since 1904. For routine climatological work, it is customary to compute approximate daily mean values for individual days from values observed at fixed hours. In the KMA, fixed hours were totally 5 times changed: at four-hourly, four-hourly interval with additional 12 hour, eight-hourly, six-hourly, three-hourly intervals. In this paper, the homogeneity in the daily mean temperature dataset of the KMA was assessed with the consistency and efficiency of point estimators. We used the daily mean calculated from the 24 hourly readings as a potential true value. Approximate daily means computed from temperatures observed at different fixed hours have statistically different properties. So this inhomogeneity in KMA climate data should be kept in mind if you want to analysis secular aspects of Korea climate using this data set.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.2
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• pp.162-170
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• 2015

Commute time embedding involves computing the spectral decomposition of the graph Laplacian. It requires the computational burden proportional to $o(n^3)$, not suitable for large scale dataset. Many methods have been proposed to accelerate the computational time, which usually employ the Nystr${\ddot{o}}$m methods to approximate the spectral decomposition of the reduced graph Laplacian. They suffer from the lost of information by dint of sampling process. This paper proposes to reduce the errors by approximating the spectral decomposition of the graph Laplacian using that of the affinity matrix. However, this can not be applied as the data size increases, because it also requires spectral decomposition. Another method called approximate commute time embedding is implemented, which does not require spectral decomposition. The performance of the proposed algorithms is analyzed by computing the commute time on the patch graph.

• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.3
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• pp.39-48
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• 2015

Even though ruin probability is a fundamental value to determine the insurance premium and policy, the complexity involved in computing its exact value forced us resort to an approximate method. In this paper, we first present an exact method to compute ruin probability under the assumption that the claim size has a GPH distribution, Then, for the arbitrary claim size distribution, we provide a method computing ruin probability quite accurately by approximating the distribution as a GPH. The validity of the proposed method demonstrated by a numerical example. The GPH approach seems to be valid for heavy-tailed claims as well as usual light-tailed claims.

• Journal of Mechanical Science and Technology
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• v.15 no.1
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• pp.125-138
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• 2001

An efficient correction storage scheme on a structured grid is applied to a sequence of approximate Jacobian systems arising at each time step from a linearization of the discrete nonlenear system of equations, obtained by the implicit time discretization of the conservation laws for unsteady fluid flows. The contribution of freezing the Jacobian matrix to computing costs is investigated within the correction storage scheme. The performance of the procedure is exhibited by measuring CPU time required to obtain a fully developed laminar vortex shedding flow past a circular cylinder, and is compared with that of a collective iterative method on a single grid. In addition, some computed results of the flow are presented in terms of some functionals along with measured data. The computational test shows that the computing costs may be saved in favor of the correction storage scheme with the frozen Jacobian matrix, to a great extent.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.317-324
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• 2008

Optimum design for general or complex structures are required to the need of many numbers of structural analyses. However, current computational environment with single processor is not capable of generating a high-level efficiency in structural analysis and design process for complex structures. In this paper, a virtual parallel computing system communicated by an internet of personal computers and workstation is constructed. In addition, a routine executing Pro/E, ANSYS and optimization algorithm automatically are adopted in the distributed process technique of sequential approximate optimization for the purpose of enhancing the flexibility of application to general structures. By employing the distributed processing technique during structural analysis using commercial application, total calculation time could be reduced, which will enhance the applicability of the proposed technique to the general complex structures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.71-78
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• 2005

In performance-based design methods, it is clear that the evaluation of the nonlinear response is required. The methods available to the design engineer today are nonlinear tim history analyses, or monotonic static nonlinear analyses, or equivalent static analyses with simulated inelastic influences. The nonlinear time analysis is the most accurate method in computing the nonlinear response of structures, but it is time-consuming and necessitate more efforts. Some codes proposed the capacity spectrum method based on the nonlinear static analysis to determine earthquake-induced demand given the structure pushover curve. This procedure is conceptually simple but iterative and time consuming with some errors. The nonlinear direct spectrum method is proposed and studied to evaluate nonlinear response of structures, without iterative computations, given by the structural linear vibration period and yield strength from the pushover analysis. The purpose of this paper is to compare the accuracy and the reliability of approximate nonlinear methods with respect to RC dual system and various earthquakes.

• JSTS:Journal of Semiconductor Technology and Science
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• v.17 no.3
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• pp.465-472
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• 2017

Security has become one of the most important requirements for various devices for multi-sensor based embedded systems. The AES (Advanced Encryption Standard) algorithm is widely used for security, however, it requires high computing power. In order to reduce the CPU power for the data encryption of images, we propose a new image encryption module using hardware memoization, which can reuse previously generated data. However, as image pixel data are slightly different each other, the reuse rate of the simple memoization system is low. Therefore, we further apply an approximate concept to the memoization system to have a higher reuse rate by sacrificing quality. With the novel technique, the throughput can be highly improved by 23.98% with 14.88% energy savings with image quality loss minimization.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.349-372
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• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.