• Title/Summary/Keyword: Mathematics error

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Empirical Bayesian Misclassification Analysis on Categorical Data (범주형 자료에서 경험적 베이지안 오분류 분석)

  • 임한승;홍종선;서문섭
    • The Korean Journal of Applied Statistics
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    • v.14 no.1
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    • pp.39-57
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    • 2001
  • Categorical data has sometimes misclassification errors. If this data will be analyzed, then estimated cell probabilities could be biased and the standard Pearson X2 tests may have inflated true type I error rates. On the other hand, if we regard wellclassified data with misclassified one, then we might spend lots of cost and time on adjustment of misclassification. It is a necessary and important step to ask whether categorical data is misclassified before analyzing data. In this paper, when data is misclassified at one of two variables for two-dimensional contingency table and marginal sums of a well-classified variable are fixed. We explore to partition marginal sums into each cells via the concepts of Bound and Collapse of Sebastiani and Ramoni (1997). The double sampling scheme (Tenenbein 1970) is used to obtain informations of misclassification. We propose test statistics in order to solve misclassification problems and examine behaviors of the statistics by simulation studies.

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Algebraic Problem Solving of the High School Students : An Analysis of Strategies and Errors (고등학교(高等學校) 학생(學生)의 대수(代數) 문제(問題) 해결(解決) : 전략(戰略)과 오류(誤謬) 분석(分析))

  • Lee, Sang-Won;Jeon, Pyung-Kook
    • Communications of Mathematical Education
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    • v.2
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    • pp.181-191
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    • 1997
  • The purpose of this study is to provide the primary sources to improve the problem solving performance by analyzing the errors and the strategies selection of the high school students when solving given algebraic problems. To attain the purpose of this study, the questions for investigation in this study are : 1. What are the differences / similarities in the patterns of errors committed by successful and unsuccessful problem-solvers when solving particular algebraic problems ? 2. What are the error types chosen by unsuccessful problem-solvers when solving particular algebraic problems? 3. Do students utilize checking, either locally or globally, when solving particular algebraic problems? Twenty students were drawn out of 10th grade students in J girls' high school in Yengi -gun, Chung-Nam, for this study. The problem-solving test was used as a test instrument. From the data, the verbal protocols and the written protocols were analyzed by the patterns. The conclusions drawn from the results obtained in the present study are as follows: First, in solving particular algebraic problems, when the problems were solved with one strategy, most students didn't give any consideration to other strategies. So mathematics teachers should teach them to use the various strategies, and should develop the problems to be used the various strategies. Second, in solving particular algebraic problems, errors on notions or transformations of equations were found. Thus, the basic knowledges related to equation should be taught. In addition, most unsuccessful students seleted the strategies inadequately to solve the problems because of misunderstanding the problems. So, to improve the problem solving performance the processes of 'understanding problem' should be emphasized to students. Third, although the unsuccesful students used the 'checking' processes when solving the problems, most of them did not find the errors because of misconceptions related to the problems, carelessness, and unskillfulness of checking. Thus, students must be taught more carefully and encouraged to use the checking.

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Review on the Extreme Didactic Phenomena in the Mathematical Class (수학 교실에서 나타나는 극단적 교수 현상에 대한 고찰)

  • Kim, Bu-Yoon;Jung, Gyeong-Mee
    • Communications of Mathematical Education
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    • v.21 no.3
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    • pp.407-430
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    • 2007
  • The extreme didactic phenomena that occur by ignoring or overemphasizing the process of personalization/contextualization, depersonalization/decontextualization of mathematical knowledge is always in our teaching practice and in fact, seems to be a kind of phenomena that suppress teachers psychologically or didactically. The study of the problems on error, misconception or obstacles revealed by students has been done continuously, but that of the extreme didactic phenomena revealed by teachers has not. In this study, I will explain four extreme didactic phenomena and help you understand them by giving various examples from several case studies and analyzing them. And also, I will discuss the way to overcome the extreme didactic phenomena in the mathematical class, based on this analysis. This thesis will become a standard of didactic phenomena that are proceeded extremely by having teachers reconsider their own classes and furthemore, will offer the research data for considering better didactic situation.

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ECG signal compression based on B-spline approximation (B-spline 근사화 기반의 심전도 신호 압축)

  • Ryu, Chun-Ha;Kim, Tae-Hun;Lee, Byung-Gook;Choi, Byung-Jae;Park, Kil-Houm
    • Journal of the Korean Institute of Intelligent Systems
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    • v.21 no.5
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    • pp.653-659
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    • 2011
  • In general, electrocardiogram(ECG) signals are sampled with a frequency over 200Hz and stored for a long time. It is required to compress data efficiently for storing and transmitting them. In this paper, a method for compression of ECG data is proposed, using by Non Uniform B-spline approximation, which has been widely used to approximation theory of applied mathematics and geometric modeling. ECG signals are compressed and reconstructed using B-spline basis function which curve has local controllability and control a shape and curve in part. The proposed method selected additional knot with each step for minimizing reconstruction error and reduced time complexity. It is established that the proposed method using B-spline approximation has good compression ratio and reconstruct besides preserving all feature point of ECG signals, through the experimental results from MIT-BIH Arrhythmia database.

Statistical Analysis of Electrical Tree Inception Voltage, Breakdown Voltage and Tree Breakdown Time Data of Unsaturated Polyester Resin

  • Ahmad, Mohd Hafizi;Bashir, Nouruddeen;Ahmad, Hussein;Piah, Mohamed Afendi Mohamed;Abdul-Malek, Zulkurnain;Yusof, Fadhilah
    • Journal of Electrical Engineering and Technology
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    • v.8 no.4
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    • pp.840-849
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    • 2013
  • This paper presents a statistical approach to analyze electrical tree inception voltage, electrical tree breakdown voltage and tree breakdown time of unsaturated polyester resin subjected to AC voltage. The aim of this work was to show that Weibull and lognormal distribution may not be the most suitable distributions for analysis of electrical treeing data. In this paper, an investigation of statistical distributions of electrical tree inception voltage, electrical tree breakdown voltage and breakdown time data was performed on 108 leaf-like specimen samples. Revelations from the test results showed that Johnson SB distribution is the best fit for electrical tree inception voltage and tree breakdown time data while electrical tree breakdown voltage data is best suited with Wakeby distribution. The fitting step was performed by means of Anderson-Darling (AD) Goodness-of-fit test (GOF). Based on the fitting results of tree inception voltage, tree breakdown time and tree breakdown voltage data, Johnson SB and Wakeby exhibit the lowest error value respectively compared to Weibull and lognormal.

Effects on the Application by Finding Errors in the Learning of Figure (도형 학습에서의 오류 찾기 활동의 적용 효과)

  • Lim, Ji-Hyun;Choi, Chang Woo
    • Education of Primary School Mathematics
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    • v.19 no.1
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    • pp.31-45
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    • 2016
  • In this study, the case of error became the object of learning, and the investigator applied these cases to an actual class and established three study problems in order to achieve the purpose of this study. The results of analysis of students' errors in figure based on before achievement test are shown as follows: First, the most errors occurred in the figure was the ones from deficient mastery of prerequisite concepts and definitions. Specially, the errors from deficient mastery of prerequisite concepts and definitions have the majority. it is very high ratio even if it considers an influence of an evaluation question item. so, I think it is necessary to teach concept related figure above all. Second, as the results of application 'finding errors' to a class, there is a meaningful difference in the mathematical achievement and reasoning ability within significance level 5%. This means 'finding errors' is one of the teaching method that it develops the mathematical achievement and reasoning ability.

The Effect of Problem-based Learning Strategies (PBL) on Problem Solving Skill: A Meta-Analysis. (문제중심학습(PBL)이 문제해결능력에 미치는 효과에 관한 메타분석)

  • Park, Il-Soo
    • Journal of the Korea Convergence Society
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    • v.10 no.10
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    • pp.197-205
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    • 2019
  • The purpose of this research was examining the effects of problem-based learning strategies(PBL) on problem solving skill conducted in Korea, using meta-analysis technique. This meta-analysis reviewed the results of 41 studies published between 1998 and 2017 in Korea. The overall weighted mean effect size value was .753 with .064 standard error which was calculated by random effects model. PBL strategies have been found to be more effective in mathematics course (d=.922), art course (d=.916), practical art course (d=.827), E-PBL (d=.791) and middle school level (d=.972). As PBL exhibit a substantial effect on students' problem solving skill, it is recommended that teachers should learn how to implement these strategies in their lesson. PBL is expected to contribute to the improvement of teaching methods as the learning environment changes during the 4th Industrial Revolution.

Truncated Differential Cryptanalysis on PP-1/64-128 (블록 암호 PP-1/64-128에 대한 부정 차분 공격)

  • Hong, Yong-Pyo;Lee, Yus-Sop;Jeong, Ki-Tae;Sung, Jae-Chul;Hong, Seok-Hie
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.21 no.6
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    • pp.35-44
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    • 2011
  • The PP-1/64-128 block cipher support variety data block and secret key size. Also, it is suitable for hardware implementation and can much easier to apply Concurrent Error Detection(CED) for cryptographic chips compared to other block ciphers, because it has same encryption and decryption process. In this paper, we proposed truncated differential cryptanalysis of PP-1/64-128. the attack on PP-1/64-128 block cipher requires $2^{50.16}$ chosen plaintexts, $2^{46.16}$ bytes memory spaces and $2^{50.45}$ PP-1/64-128 encryption to retrieve secret key. This is the best result of currently known PP-1/64-128 differential cryptanalysis.

Factor augmentation for cryptocurrency return forecasting (암호화폐 수익률 예측력 향상을 위한 요인 강화)

  • Yeom, Yebin;Han, Yoojin;Lee, Jaehyun;Park, Seryeong;Lee, Jungwoo;Baek, Changryong
    • The Korean Journal of Applied Statistics
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    • v.35 no.2
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    • pp.189-201
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    • 2022
  • In this study, we propose factor augmentation to improve forecasting power of cryptocurrency return. We consider financial and economic variables as well as psychological aspect for possible factors. To be more specific, financial and economic factors are obtained by applying principal factor analysis. Psychological factor is summarized by news sentiment analysis. We also visualize such factors through impulse response analysis. In the modeling perspective, we consider ARIMAX as the classical model, and random forest and deep learning to accommodate nonlinear features. As a result, we show that factor augmentation reduces prediction error and the GRU performed the best amongst all models considered.

Object Recognition Using Convolutional Neural Network in military CCTV (합성곱 신경망을 활용한 군사용 CCTV 객체 인식)

  • Ahn, Jin Woo;Kim, Dohyung;Kim, Jaeoh
    • Journal of the Korea Society for Simulation
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    • v.31 no.2
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    • pp.11-20
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    • 2022
  • There is a critical need for AI assistance in guard operations of Army base perimeters, which is exacerbated by changes in the national defense and security environment such as force reduction. In addition, the possibility for human error inherent to perimeter guard operations attests to the need for an innovative revamp of current systems. The purpose of this study is to propose a real-time object detection AI tailored to military CCTV surveillance with three unique characteristics. First, training data suitable for situations in which relatively small objects must be recognized is used due to the characteristics of military CCTV. Second, we utilize a data augmentation algorithm suited for military context applied in the data preparation step. Third, a noise reduction algorithm is applied to account for military-specific situations, such as camouflaged targets and unfavorable weather conditions. The proposed system has been field-tested in a real-world setting, and its performance has been verified.