• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

• Genomics & Informatics
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• 제21권1호
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• pp.15.1-15.4
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• 2023

Bioinformatics education can be defined as the teaching and learning of how to use software tools, along with mathematical and statistical analysis, to solve biological problems. Although many resources are available, most students still struggle to understand even the simplest sequence alignment algorithms. Applying visualizations to these topics benefits both lecturers and students. Unfortunately, educational software for visualizing step-by-step processes in the user experience of sequence alignment algorithms is rare. In this article, an educational visualization tool for biological sequence alignment is presented, and the source code is released in order to encourage the collaborative power of open-source software, with the expectation of further contributions from the community in the future. Two different modules are integrated to enable a student to investigate the characteristics of alignment algorithms.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권4호
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• pp.433-452
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• 2018

The purpose of this study is to provide implications for improvement of mathematics textbook based on discursive approach to textbook analysis that complementarily combines a communicational approach to cognition and social semiotics. For this purpose, we reconstructed an analytic framework for discursive approach to written discourses of Korean textbook and CMP, and applied it to our analysis. Results show that several characteristics in meanings were developed by the use of words and visual mediators. First, in the case of ideational meaning, there were qualitative and quantitative differences between vocabularies used and between information addressed by visual mediators. Second, in the case of structural meaning, an offer and application of procedure was emphasized in a Korean textbook, whereas expectation and selection experiences of diverse possibilities for problem solving was underlined in CMP. In the case interpersonal meaning of student-author, imperative instructions were paid attentions in a Korean textbook. In contrast, students' interdependence and active participation were stressed in CMP. Therefore, this study addressed ideas about how to analyze mathematics textbooks based on integrated meanings developed by the use of words and visual mediators. In addition, it distributes implications for improvements of Korean mathematics textbooks through the analytic framework of both mathematical meanings and interpersonal meanings of student-author.

• 대한전자공학회논문지SD
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• 제46권8호
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• pp.102-116
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• 2009

최근 멀티코어 프로세서의 이용이 증가함에 따라, 멀티코어환경에서 고성능 H.264/AVC 코덱을 구현하기 위한 다양한 병렬화 기법들이 제안되고 있다. 이러한 기법들은 병렬화 기법 적용 방식에 따라 태스크 레벨 병렬화 기법과 데이터 레벨 병렬화 기법으로 구분된다. 태스크 레벨 병렬화 기법을 이용한 파이프라인 병렬화 기법은 H.264 알고리즘을 파이프라인 단계로 나누어 구현하며, 일반적으로 화면 사이즈가 작고 복잡도가 낮은 비트스트림에 유리하다. 그러나 프로세싱 모듈별 수행시간 차이가 커서 로드밸런싱이 좋지 않고, 파이프라인 단계의 수가 제한적이라 성능 확장성에 제한이 있어 HD 비디오같이 해상도가 큰 비트스트림 처리에는 적합하지 않은 단점이 있다. 본 논문에서는 로드밸런싱 및 성능 확장성을 고려하여 매크로블록 라인 단위로 쓰레드를 할당하는 수평적 데이터 레벨 병렬화 기법을 제안하고, 이에 대한 성능 예측 수식 모델을 통하여 성능을 예상한다. 또한 성능 예측의 정확성을 검증하기 위해 JM 13.2 레퍼런스 디코더에 대한 데이터 레벨 병렬화 기법을 ARM11 MPCore 환경에서 구현하고 이에 대한 성능 검증을 수행하였다. SoCDesigner를 이용한 사이클 단위의 성능 측정 결과, 본 논문에서 제시하는 쓰레드 증가에 대한 병렬화 기법의 성능 변화를 비교적 높은 수준의 정확도로 예측 가능하였다.

• 대한수학교육학회지:학교수학
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• 제15권3호
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• pp.603-617
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• 2013

본 연구는 개인의 의사결정 과정에서 자신이 가지고 있는 확률적 지식과 자신이 선택한 결과 사이에 간극이 발생하는 현상을 분석해 봄으로써 수학영재학생들을 위한 확률문제 지도시 고려해야 할 점들을 알아보는 것이다. 이를 위해 23명의 6학년 수학영재 학생들에게 확률과 기댓값의 개념이 내재된 확률 문제 5개(조건이 하나씩 변하는 시리즈)를 제시하고 그들의 선택에 영향을 미친 요인들을 분석하고 이를 시각화하였다. 초등수학영재학생들이 선택한 결과와 그 근거에 대한 분석은 수업 관찰 및 비디오 분석, 학습지 분석, 그리고 관찰자의 면담의 삼각분석법을 사용하였다. 결과 분석을 통하여 영재학생들에게 확률 문제를 지도할 때 고려해야 할 교육적 시사점을 제시하였다.

• 대한수학회지
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• 제54권4호
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• 대한수학회보
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• 제53권5호
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• 영재교육연구
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• 제19권1호
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• pp.47-67
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• 2009

본 논문은 유전적 요소가 비슷한 형제 영재에 관한 사례연구이다. 본 연구자는 이들 형제가 3년간 이수한 영재교육원의 강사로 활동하면서 같은 과정의 수업시간에 나타난 두 형제의 상이한 수학적 성향에 관심을 갖고 두 형제의 자라온 환경과 부모의 기대, 양육태도 등 영재성에 영향을 주는 환경적인 요소 등을 연구 참여자와 부모의 면담을 통하여 비교 분석하였다. 부모는 일찍이 영재성을 드러낸 형에게 많은 기대와 지원을 한 만큼 강압적인 양육태도로 일관했으나 뒤늦게 영재성을 보인 동생에겐 자율적인 양육태도로 스스로 학습을 원하는 시기에 지원하였다. 그러한 결과 동생이 오히려 창의적인 사고와 학업 성취도에서 좋은 결과를 보여주었다. 본 형제연구는 자녀의 영재성을 극대화시키기 위한 부모의 긍정적인 양육태도에 대한 하나의 시사점을 제공하는 데 그 의의를 둘 수 있다.

• 한국농공학회논문집
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• 제49권2호
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• pp.61-74
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• 2007

A mathematical modeling program called Hydrological Simulation Program-FORTRAN (HSPF) developed by the United States Environmental Protection Agency (EPA) was applied to Hwaseong watershed. It was run under BASINS (Better Assessment Science for Integrating Point and Nonpoint Sources) program, and the model was validated using monitoring data of $2002{\sim}2005$. The model efficiency of runoff ranged from good to fair in comparison between simulated and observed data, while it was from very good to poor in the water quality parameters. But its reliability and performance were within the expectation considering complexity of the watershed and pollutant sources. The nonpoint source (NPS) loading for T-N and T-P during the monsoon rainy season (June to September) was about 80% of total NPS loading, and runoff volume was also in a similar range. However, NPS loading for BOD ($55{\sim}60%$) didn't depend on rainfall because BOD was mostly discharged from point source (more than 70%). And water quality was not necessarily high during the rainy season, and showed a decreasing trend with increasing water flow. BASINS/HSPF was applied to the Hwaseong watershed successfully without difficulty, and it was found that the model could be used conveniently to assess watershed characteristics and to estimate pollutant loading including point and nonpoint sources in watershed scale.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권3호
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• pp.1083-1097
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• 2018

This paper presents a novel range-free localization algorithm based on quantum particle swarm optimization. The proposed algorithm is capable of estimating the distance between two non-neighboring sensors for multi-hop heterogeneous wireless sensor networks where all nodes' communication ranges are different. Firstly, we construct a new cumulative distribution function of expected hop progress for sensor nodes with different transmission capability. Then, the distance between any two nodes can be computed accurately and effectively by deriving the mathematical expectation of cumulative distribution function. Finally, quantum particle swarm optimization algorithm is used to improve the positioning accuracy. Simulation results show that the proposed algorithm is superior in the localization accuracy and efficiency when used in random and uniform placement of nodes for heterogeneous wireless sensor networks.