• Genomics & Informatics
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• 제20권1호
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• pp.9.1-9.6
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• 2022

Mendelian randomization (MR) uses genetic variation as a natural experiment to investigate the causal effects of modifiable risk factors (exposures) on outcomes. Two-sample Mendelian randomization (2SMR) is widely used to measure causal effects between exposures and outcomes via genome-wide association studies. 2SMR can increase statistical power by utilizing summary statistics from large consortia such as the UK Biobank. However, the first-order term approximation of standard error is commonly used when applying 2SMR. This approximation can underestimate the variance of causal effects in MR, which can lead to an increased false-positive rate. An alternative is to use the second-order approximation of the standard error, which can considerably correct for the deviation of the first-order approximation. In this study, we simulated MR to show the degree to which the first-order approximation underestimates the variance. We show that depending on the specific situation, the first-order approximation can underestimate the variance almost by half when compared to the true variance, whereas the second-order approximation is robust and accurate.

• 한국공작기계학회논문집
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• 제12권2호
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• pp.9-16
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• 2003

A strategy of the optimal shape design with FEA(Finite Element Analysis) for 2-D structure is proposed by comparing subproblem approximation method with first order approximation method. A cantilever beam with two different loading conditions, a concentrated load and an evenly distribute load, and truss structure with a concentrated loading condition are implemented to optimize the shape. It gives a good design strategy on the optimal truss structure as well as the optimal cantilever beam shape. It is found that the convergence is quickly finished with the iteration number below ten. Optimized shapes of cantilever beam and truss structure are shown with stress contour plot by the results of the subproblem approximation method and the first order approximation methd.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1997년도 추계학술발표회논문집(1)
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• pp.85-90
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• 1997

Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of our approximation, these approximate results are compared with exact results obtained from our previous numerical study.

• ETRI Journal
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• 제37권4호
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• pp.727-735
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• 2015

This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first-order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second-order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first-order Taylor approximation to suit higher-order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first-order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal-to-noise ratio conditions, respectively.

• 한국전산구조공학회논문집
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• 제31권6호
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• pp.331-337
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• 2018

본 논문은 MLS(moving least squares) 차분법의 1차 미분 근사함수를 바탕으로 시간에 따른 수치해석이 가능한 해석기법을 제시한다. 오직 1차 미분 근사함수로만 지배방정식을 이산화했으며, 근사함수를 조립하는 형태로 전체 시스템 방정식을 구성하여 차분법으로 이산화된 운동방정식이 유한요소법(finite element method)과 유사한 모습을 갖게 되었다. 운동방정식을 시간적분하기 위해서 중앙차분법(central difference method)을 사용하였다. 유한요소 알고리즘을 통해서 MLS 차분법과 유한요소법의 고유진동 해석을 수행하였으며, 두 해석결과를 비교하였다. 또한, 동적해석 결과를 기존의 2차 미분 근사함수를 활용한 해석결과와 함께 도시함으로써 제안된 수치기법의 정확성을 검증하였다. 1차 미분 근사함수를 조립하는 과정에서 해석결과의 떨림현상이 억제되었으며 상대적으로 균일한 응력분포를 구할 수 있었다.

• 전력전자학회:학술대회논문집
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• 전력전자학회 1998년도 연구회 합동 학술발표회 논문집
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• pp.73-77
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• 1998

The conventional sliding mode controller (SMCr) approach is often impractical or difficult when applied to high order process because the number of tuning parameters in the SMCr increases with the order of the plant. Camacho(1996) proposed the design of a fixed structure sliding mode controller based on a first order plus dead time approximation to the higher-order process. But, there are such problems as overshoot, settling time and command following. They are mainly due to the approximation errors of the time delay term by Taylor series. In this paper, in order to improve Camcho's method, a new Taylor approximation technique considering a weight is proposed.

• Structural Engineering and Mechanics
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• 제65권5호
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• pp.513-521
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• 2018

In this paper, the resonance response of spar-type floating platform in coupled heave and pitch motion is investigated using a CPU time-effective numerical method. A coupled nonlinear 2-DOF equation of motion is derived based on the potential wave theory and the rigid-body hydrodynamics. The transient responses are solved by the fourth-order Runge-Kutta (RK4) method and transformed to the frequency responses by the digital Fourier transform (DFT), and the first-order approximation of heave response is analytically derived. Through the numerical experiments, the theoretical derivation and the numerical formulation are verified from the comparison with the commercial software AQWA. And, the frequencies of resonance arising from the nonlinear coupling between heave and pitch motions are investigated and justified from the comparison with the analytically derived first-order approximation of heave response.

• 대한전자공학회논문지
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• 제23권5호
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• pp.647-652
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• 1986

The controller tuning methods proposed by Yuwana-Seborg and Suh utilizes Pade first order approximation for the delay terms in the closed loop transfer function. In this paper, the use of a Pade second-order approximation method is investigated. The simulation results show that the new method is superior to pervious approaches such as Ziegler-Nichols and Cohen-Coon methods.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• 전자공학회논문지A
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• 제32A권1호
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• pp.45-52
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• 1995

A new Kirchhoff approximation(KA) method was proposed for microwave scttering from randomly rough surfaces. Using the spectral representation of delta function and its sifting theorem, a new KA was formulated directly without any further approximation, and this formulated was used to compute exact backscttering coefficients. The validity of the KA was verified by a numerical method, and this new KA technique was used to evaluate the existing approximated KkA methods; i.t., the zeroth-order and the first-order approximated physical optics(PO) models. It was shown that the first-order approximated PO model has small error than the zeroth-order approximated PO model at low incidence angles and the opposite happens at higher incidence angles. This new KA model can be used to compute exact scattering coefficients in the validity regions of KA and to evaluate other theoretical and numerical models for scattering from randomly rough surfaces.