• 제목/요약/키워드: Mathematics error

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서남해안 관측자료를 활용한 OI 자료동화의 최적 매개변수 산정 연구 (Experimental Study of Estimating the Optimized Parameters in OI)

  • 구본호;우승범;김상일
    • 한국해안·해양공학회논문집
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    • 제31권6호
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    • pp.458-467
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    • 2019
  • 본 연구는 자료동화에 필요한 매개변수의 최적화된 값를 산정하기 위해 서남해안을 포함하는 한반도 중심해역에 해양순환수치모델 FVCOM(Finite Volume Community Ocean Model)을 구축 및 검증하고 이에 연속관측된 수층별 유속자료와 OI(Optimal Interpolation)를 자료동화하였다. 자료동화에는 서남해안에 위치한 4정점에서 ADCP(Acoustic Doppler Current Profiler)을 통해 관측된 수층별 유속자료를 사용하였다. 자료동화에 사용된 배경 모델은 복잡하고 불규칙한 지형적 특성을 가진 서남해안 중심의 한반도 해역을 비구조격자체계의 해양순환수치모델인 FVCOM으로 구성하고 이를 조석검증하였다. 최적내삽법의 Correlation length와 Scale factor는 자료동화 과정에서 관측값의 영향 범위를 결정하고 오차를 보정할 수 있는 매개변수다. 자료동화기법 내 매개변수는 연구 지역에 존재하는 해양학적 특성에 따라 능동적으로 변동되기 때문에 이를 토대로 경험적인 산정 연구가 필요하다. 따라서 서남해안에서 요구되는 각 매개변수들을 Taylor diagram을 활용하여 관측정점별로 분석하고 최적값을 산정하였다. 산정된 최적매개변수는 관측정점마다 요구되는 값이 상이하며 연안에서 외해로 갈수록 증가하는 추세를 보인다. 추가로 조석검증 전과 후에 따른 배경 모델이 갖는 정확성이 자료동화 효과에 미치는 영향을 분석하였다. 조석검증을 통해 정확성이 높아진 배경 모델은 배경오차공분산이 상대적으로 감소됨에 따라서 총 비중 함수가 0에 가까워지고 결과적으로 최적매개변수값이 감소하였다. 이러한 최적매개변수는 광역 모델이 갖고 있는 연안역까지 도달하는 개방경계의 한계점을 완화시켜줄 것으로 기대하며 향후 관측정점별로 요구되는 최적매개변수값을 독립적으로 적용하도록 개선한다면 향상된 해양예측 시스템 개발에 도움이 될 것으로 기대한다.

Distance Measurement Using a Single Camera with a Rotating Mirror

  • Kim Hyongsuk;Lin Chun-Shin;Song Jaehong;Chae Heesung
    • International Journal of Control, Automation, and Systems
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    • 제3권4호
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    • pp.542-551
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    • 2005
  • A new distance measurement method with the use of a single camera and a rotating mirror is presented. A camera in front of a rotating mirror acquires a sequence of reflected images, from which distance information is extracted. The distance measurement is based on the idea that the corresponding pixel of an object point at a longer distance moves at a higher speed in a sequence of images in this type of system setting. Distance measurement based on such pixel movement is investigated. Like many other image-based techniques, this presented technique requires matching corresponding points in two images. To alleviate such difficulty, two kinds of techniques of image tracking through the sequence of images and the utilization of multiple sets of image frames are described. Precision improvement is possible and is one attractive merit. The presented approach with a rotating mirror is especially suitable for such multiple measurements. The imprecision caused by the physical limit could be improved through making several measurements and taking an average. In this paper, mathematics necessary for implementing the technique is derived and presented. Also, the error sensitivities of related parameters are analyzed. Experimental results using the real camera-mirror setup are reported.

Two Messages out of One 2D Matrix Bar Code

  • Cvitic, Filip;Pavcevic, Mario Osvin;Pibernik, Jesenka
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제9권3호
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    • pp.1105-1120
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    • 2015
  • With the proposed principle of two-dimensional matrix bar code design based on masks, the whole surface of a 2D bar code is used for creating graphic patterns. Masks are a method of overlaying certain information with complete preservation of encoded information. In order to ensure suitable mask performance, it is essential to create a set of masks (mask folder) which are similar to each other. This ultimately allows additional error correction on the whole code level which is proven mathematically through an academic example of a QR code with a matrix of size $9{\times}9$. In order to create a mask folder, this article will investigate parameters based on Weber's law. With the parameters founded in the research, this principle shows how QR codes, or any other 2D bar code, can be designed to display two different messages. This ultimately enables a better description of a 2D bar code, which will improve users' visual recognition of 2D bar code purpose, and therefore users' greater enjoyment and involvement.

Extending the Scope of Automatic Time Series Model Selection: The Package autots for R

  • Jang, Dong-Ik;Oh, Hee-Seok;Kim, Dong-Hoh
    • Communications for Statistical Applications and Methods
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    • 제18권3호
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    • pp.319-331
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    • 2011
  • In this paper, we propose automatic procedures for the model selection of various univariate time series data. Automatic model selection is important, especially in data mining with large number of time series, for example, the number (in thousands) of signals accessing a web server during a specific time period. Several methods have been proposed for automatic model selection of time series. However, most existing methods focus on linear time series models such as exponential smoothing and autoregressive integrated moving average(ARIMA) models. The key feature that distinguishes the proposed procedures from previous approaches is that the former can be used for both linear time series models and nonlinear time series models such as threshold autoregressive(TAR) models and autoregressive moving average-generalized autoregressive conditional heteroscedasticity(ARMA-GARCH) models. The proposed methods select a model from among the various models in the prediction error sense. We also provide an R package autots that implements the proposed automatic model selection procedures. In this paper, we illustrate these algorithms with the artificial and real data, and describe the implementation of the autots package for R.

Machine Learning Based Automatic Categorization Model for Text Lines in Invoice Documents

  • Shin, Hyun-Kyung
    • 한국멀티미디어학회논문지
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    • 제13권12호
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    • pp.1786-1797
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    • 2010
  • Automatic understanding of contents in document image is a very hard problem due to involvement with mathematically challenging problems originated mainly from the over-determined system induced by document segmentation process. In both academic and industrial areas, there have been incessant and various efforts to improve core parts of content retrieval technologies by the means of separating out segmentation related issues using semi-structured document, e.g., invoice,. In this paper we proposed classification models for text lines on invoice document in which text lines were clustered into the five categories in accordance with their contents: purchase order header, invoice header, summary header, surcharge header, purchase items. Our investigation was concentrated on the performance of machine learning based models in aspect of linear-discriminant-analysis (LDA) and non-LDA (logic based). In the group of LDA, na$\"{\i}$ve baysian, k-nearest neighbor, and SVM were used, in the group of non LDA, decision tree, random forest, and boost were used. We described the details of feature vector construction and the selection processes of the model and the parameter including training and validation. We also presented the experimental results of comparison on training/classification error levels for the models employed.

복합 분위수 회귀에 대한 붓스트랩 방법의 응용 (Bootstrapping Composite Quantile Regression)

  • 서강민;방성완;전명식
    • 응용통계연구
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    • 제25권2호
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    • pp.341-350
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    • 2012
  • 선형 회귀모형에서 오차항들이 서로 독립이고 동일한 분포를 따른다고 가정할 경우, (회귀계수의 강건한 추정을 위하여) 모든 분위수 함수의 회귀계수가 동일한 값을 갖는다는 사실에 근거한 복합 분위수 회귀(composite quantile regression) 방법을 고려할 수 있다. 본 논문에서는 복합 분위수 회귀에서 사용되는 분위수의 개수를 선택하기 위해 붓스트랩 방법의 가능성을 검토하였다. 또한, 분위수 회귀와 복합 분위수 회귀의 성능을 비교하기 위해 붓스트랩 방법을 이용하여 신뢰구간을 구축하고, 이들의 포함확률과 평균길이를 비교하였다. 이러한 모의실험을 통하여 복합 분위수 회귀의 우월성과 통계적 추론에 있어서 붓스트랩 방법의 유용성을 확인하였다.

Customer Order Scheduling Problems with a Fixed Machine-Job Assignment

  • Yang, Jae-Hwan;Rho, Yoo-Mi
    • Management Science and Financial Engineering
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    • 제11권2호
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    • pp.19-43
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    • 2005
  • This paper considers a variation of the customer order scheduling problem, and the variation is the case where the machine-job assignment is fixed. We examine the parallel machine environment, and the objective is to minimize the sum of the completion times of the batches. While a machine can process only one job at a time, different machines can simultaneously process different jobs in a batch. The recognition version of this problem is known to be NP-complete in the strong sense even if there exist only two parallel machines. When there are an arbitrary number of parallel machines, we establish three lower bounds and develop a dynamic programming (DP) algorithm which runs in exponential time on the number of batches. We present two simple but intuitive heuristics, SB and GR, and find some special cases where SB and GR generate an optimal schedule. We also find worst case upper bounds on the relative error. For the case of the two parallel machines, we show that GR generates an optimal schedule when processing times of all batches are equal. Finally, the heuristics and the lower bounds are empirically evaluated.

FAULT DETECTION, MONITORING AND DIAGNOSIS OF SEQUENCING BATCH REACTOR FOR INTEGRATED WASTEWATER TREATMENT MANAGEMENT SYSTEM

  • Yoo, Chang-Kyoo;Vanrolleghem, Peter A.;Lee, In-Beum
    • Environmental Engineering Research
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    • 제11권2호
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    • pp.63-76
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    • 2006
  • Multivariate analysis and batch monitoring on a pilot-scale sequencing batch reactor (SBR) are described for integrated wastewater treatment management system, where a batchwise multiway independent component analysis method (MICA) are used to extract meaningful hidden information from non-Gaussian wastewater treatment data. Three-way batch data of SBR are unfolded batch-wisely, and then a non-Gaussian multivariate monitoring method is used to capture the non-Gaussian characteristics of normal batches in biological wastewater treatment plant. It is successfully applied to an 80L SBR for biological wastewater treatment, which is characterized by a variety of error sources with non-Gaussian characteristics. The batchwise multivariate monitoring results of a pilot-scale SBR for integrated wastewater treatment management system showed more powerful monitoring performance on a WWTP application than the conventional method since it can extract non-Gaussian source signals which are independent and cross-correlation of variables.

특이발현과 특이공발현을 고려한 유의한 유전자 집단 탐색 (Identifying statistically significant gene sets based on differential expression and differential coexpression)

  • 이선호
    • 응용통계연구
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    • 제29권3호
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    • pp.437-448
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    • 2016
  • 서로 상관있는 유전자들의 발현조절이 질병이나 종양의 발생에 영향을 미치기 때문에 단일유전자 분석 대신 공통의 생물학적 요소를 지닌 유전자 집단 분석이 각광을 받게 되었고 생물학적으로 좀더 설명하기 쉬운 결과를 얻게 되었다. 표현형에 따라 유의한 차이를 보이는 유전자 집단을 찾는 여러 방법들이 있지만, 대부분의 방법들이 집단에 속한 유전자들의 표현형에 따른 발현의 차이를 탐색하거나 유전자들 사이의 공발현 구조가 다른지 탐색하는 것이다. 본 연구에서는 특이발현과 특이공발현의 차이를 모두 고려하는 탐색방법을 제시하였고 p53이란 유전자 자료와 모의자료를 이용하여 제시한 방법의 성능을 알아 보았다.

Efficiency and Robustness of Fully Adaptive Simulated Maximum Likelihood Method

  • Oh, Man-Suk;Kim, Dai-Gyoung
    • Communications for Statistical Applications and Methods
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    • 제16권3호
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    • pp.479-485
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    • 2009
  • When a part of data is unobserved the marginal likelihood of parameters given the observed data often involves analytically intractable high dimensional integral and hence it is hard to find the maximum likelihood estimate of the parameters. Simulated maximum likelihood(SML) method which estimates the marginal likelihood via Monte Carlo importance sampling and optimize the estimated marginal likelihood has been used in many applications. A key issue in SML is to find a good proposal density from which Monte Carlo samples are generated. The optimal proposal density is the conditional density of the unobserved data given the parameters and the observed data, and attempts have been given to find a good approximation to the optimal proposal density. Algorithms which adaptively improve the proposal density have been widely used due to its simplicity and efficiency. In this paper, we describe a fully adaptive algorithm which has been used by some practitioners but has not been well recognized in statistical literature, and evaluate its estimation performance and robustness via a simulation study. The simulation study shows a great improvement in the order of magnitudes in the mean squared error, compared to non-adaptive or partially adaptive SML methods. Also, it is shown that the fully adaptive SML is robust in a sense that it is insensitive to the starting points in the optimization routine.