• 제목/요약/키워드: Mathematics error

검색결과 758건 처리시간 0.026초

Multinomial Group Testing with Small-Sized Pools and Application to California HIV Data: Bayesian and Bootstrap Approaches

  • 김종민;허태영;안형진
    • 한국조사연구학회:학술대회논문집
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    • 한국조사연구학회 2006년도 춘계학술대회 발표논문집
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    • pp.131-159
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    • 2006
  • This paper consider multinomial group testing which is concerned with classification each of N given units into one of k disjoint categories. In this paper, we propose exact Bayesian, approximate Bayesian, bootstrap methods for estimating individual category proportions using the multinomial group testing model proposed by Bar-Lev et al (2005). By the comparison of Mcan Squre Error (MSE), it is shown that the exact Bayesian method has a bettor efficiency and consistency than maximum likelihood method. We suggest an approximate Bayesian approach using Markov Chain Monte Carlo (MCMC) for posterior computation. We derive exact credible intervals based on the exact Bayesian estimators and present confidence intervals using the bootstrap and MCMC. These intervals arc shown to often have better coverage properties and similar mean lengths to maximum likelihood method already available. Furthermore the proposed models are illustrated using data from a HIV blooding test study throughout California, 2000.

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초등학생의 사칙계산 문장제 해결 보정교육을 위한 기초 연구 (Survey for the Remedial Instruction on Arithmetic Word Problems Solving of Elementary School Students)

  • 이봉주;문승호
    • 한국수학교육학회지시리즈C:초등수학교육
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    • 제10권2호
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    • pp.141-149
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    • 2007
  • It is undeniably important to bring up a solution capability of arithmetic word problems in the elementary mathematical education. The goal of this study is to acquire the implication for remedial instruction on arithmetic word problems solving through surveying elementary school students' difficulties in the solving of arithmetic word problems. In order to do it, this study was intended to analyze the following two aspects. First, it was analyzed that they generally felt more difficulties in which field among addition, subtraction, multiplication and division word problems. Second, with the result of the first analysis, it was examined that they solved it by imagining as which sphere of the other word problems. Also, the cause of their error on the word problem solving was analyzed by the interview. From the foregoing analyses, the following implications for remedial instruction on arithmetic word problems solving are acquired. First, the accumulation of learning deficiency must be diminished through the remedial instruction. Second, it must help students to understand the given problem and to make of what the goal of problem is. Third, it must help students to form a good habit for reading the problem and to understand the context of problem. forth, the teacher must help students to review and reflect their problem-solving processes.

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증명에서 경험적 관점의 한계에 대한 중학교 3학년 학생들의 이해 연구 (A study on the understanding of limitations of experiential viewpoints for 9th grade students)

  • 노은환;강정기
    • 한국수학교육학회지시리즈A:수학교육
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    • 제54권1호
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    • pp.13-30
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    • 2015
  • The mathematical object is conceptual. Thus we can not prove the property of mathematical object in experimental viewpoint but in conceptual viewpoint. We performed the experiment for 28 middle school students to investigate whether they understand this. As a result, the majority of student didn't cognize the limit of experimental method. We had also individual interviews with four students. As results, one student was exactly cognizing the limit of experimental method, but he couldn't prove logically. The others didn't cognize the limit of experimental method. They thought that the proposition was already true regardless of the error. And one of them even thought that to be equal approximately was the same of to be equal exactly. Also, one student has confused between the experimental viewpoint and the conceptual viewpoint. This implies that it is necessary to help students understand the limit of experimental method.

컴퓨터 表示 可能數에 관하여

  • 이기호
    • 정보과학회지
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    • 제1권1호
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    • pp.75-79
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    • 1983
  • 現代 컴퓨터의 연산장치(Arithmetic unit)의 design을 하는데 있어서 가장 중요하게 요구점점되는 點은 계산의 속도(Computational speed)와 計算의 정확성 (Computational accuracy)이라고 보겠다. 여기서는 정보처리기(Information processor)로서 또는 非數理的인 연산(Non-numeric operation)을 위한 도구로서 보다는 數理的 연산(Arithmetic)을 수행하는 도구로서의 컴퓨터 연산에 限해서만 論하고자 한다. 대개의 경우 기계를 고안하는 사람들은 계사의 속도에 對해서는 특별한 관심을 갖고 그러한 목적에 맞는 기계를 만들어 낼려고 하지만 數値의 정 확성(Numerical accuracy)에 對해서ㅡ 등한시했던 경우가 많았다고 보겠다. 그러 나 이 두 條件 즉 빠른 속도 틀림없는 정확성을 同時에 충족 시키고자 하는 것이 기계 고안자들의 理想 목포가 되는 것은 사시링다. 여기에 수반도는 문제는 제작 비를 고려하지 않을 수 없다는 것이다. 정화하고 빠른 operation을 할 수 있는 기 계는 너무 비싼 제작비가 들기 때문에 사용목적에 적절하게 두 문제를 절충하여 고려하는 것이 일반적이라 하겠다. 初期의 컴퓨터는 한 Word(Computer Word)로 서 36개의 bit를 사용한 것이 많았다고 본다. 그러나 1961년 4月 Tennessee에서 Oak Riage National Laboratory와 The Society for Industril and Applied Mathematics 후원하에 일주일에 걸친 국제회의가 열렸었는데 거기 모인 거의 모 든 學者들이 앞으로의 과학 연구용 컴퓨터(Scientific Computer)의 한 Word의 길 이는 적어도 48bit 이상으로 증가시켜야 된다는데 의견을 모았었다고 한다. 이제 rounding error의 성향(begavior)을 알아보기 위한 간단한 例를 들어 봄으로써 이 글을 쓰는 동기으 일면을 대신하고자 한다.

Optimization-based Image Watermarking Algorithm Using a Maximum-Likelihood Decoding Scheme in the Complex Wavelet Domain

  • Liu, Jinhua;Rao, Yunbo
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제13권1호
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    • pp.452-472
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    • 2019
  • Most existing wavelet-based multiplicative watermarking methods are affected by geometric attacks to a certain extent. A serious limitation of wavelet-based multiplicative watermarking is its sensitivity to rotation, scaling, and translation. In this study, we propose an image watermarking method by using dual-tree complex wavelet transform with a multi-objective optimization approach. We embed the watermark information into an image region with a high entropy value via a multiplicative strategy. The major contribution of this work is that the trade-off between imperceptibility and robustness is simply solved by using the multi-objective optimization approach, which applies the watermark error probability and an image quality metric to establish a multi-objective optimization function. In this manner, the optimal embedding factor obtained by solving the multi-objective function effectively controls watermark strength. For watermark decoding, we adopt a maximum likelihood decision criterion. Finally, we evaluate the performance of the proposed method by conducting simulations on benchmark test images. Experiment results demonstrate the imperceptibility of the proposed method and its robustness against various attacks, including additive white Gaussian noise, JPEG compression, scaling, rotation, and combined attacks.

Relationships between Inbound Tourism, Financial Development, and Economic Growth: An Empirical Study of Fujian Province, China

  • An Lin, LIU;Yong Cen, LIU
    • The Journal of Asian Finance, Economics and Business
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    • 제10권2호
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    • pp.213-222
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    • 2023
  • This paper mainly studies the relationship between financial development, inbound tourism development, and economic growth rate in Fujian Province, China. This study uses the data of real GDP, foreign exchange income from international tourism, and financial interrelations ratio from 1994 to 2019. In the analysis process, the Johansen cointegration test is first used to analyze whether the three have a long-term equilibrium relationship. Then the vector error correction model is established to test the restrictive relationship among the three. Next, the Granger causality test assesses whether the three have a causal relationship. Finally, the contribution rate of the three is analyzed by variance decomposition. The above methods show the following conclusions: first, the three have a long-term equilibrium relationship. Secondly, in the short term, local economic growth is constrained by inbound tourism and financial development. Thirdly, there is a causal relationship between economic growth and inbound tourism in Fujian, while there is a unidirectional causal relationship between financial development and economic growth, financial development, and inbound tourism. Fourthly, the contribution rate of inbound tourism to economic growth fluctuations in Fujian is higher than that of financial development.

SNS 채팅 데이터에 적응적인 Self-Attention 기반 문맥의존 철자오류 교정 시스템 (Adaptive Context-Sensitive Spelling Error Correction System Based on Self-Attention for Social Network Service Chatting Data)

  • 최혜원;장대식;손동철;이승욱;고영중
    • 한국정보과학회 언어공학연구회:학술대회논문집(한글 및 한국어 정보처리)
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    • 한국정보과학회언어공학연구회 2019년도 제31회 한글 및 한국어 정보처리 학술대회
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    • pp.362-367
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    • 2019
  • 본 논문에서는 Self-Attention을 활용한 딥러닝 기반 문맥의존 철자오류 교정 모델을 제안한다. 문맥의존 철자오류 교정은 최근 철자오류 교정 분야에서 활발히 연구되고 있는 문제 중 하나이다. 기존에는 규칙 기반, 확률 기반, 임베딩을 활용한 철자오류 교정이 연구되었으나, 아직 양질의 교정을 수행해내기에는 많은 문제점이 있다. 따라서 본 논문에서는 기존 교정 모델들의 단점을 보완하기 위해 Self-Attention을 활용한 문맥의존 철자오류 교정 모델을 제안한다. 제안 모델은 Self-Attention을 활용하여 기존의 임베딩 정보에 문맥 의존적 정보가 반영된 더 나은 임베딩을 생성하는 역할을 한다. 전체 문장의 정보가 반영된 새로운 임베딩을 활용하여 동적으로 타겟 단어와의 관련 단어들을 찾아 문맥의존 철자 오류교정을 시행한다. 본 논문에서는 성능평가를 위해 세종 말뭉치를 평가 데이터로 이용하여 제안 모델을 실험하였고, 비정형화된 구어체(Kakao Talk) 말뭉치로도 평가 데이터를 구축해 실험한 결과 비교 모델보다 높은 정확율과 재현율의 성능향상을 보였다.

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A new conjugate gradient method for dynamic load identification of airfoil structure with randomness

  • Lin J. Wang;Jia H. Li;You X. Xie
    • Structural Engineering and Mechanics
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    • 제88권4호
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    • pp.301-309
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    • 2023
  • In this paper, a new modified conjugate gradient (MCG) method is presented which is based on a new gradient regularizer, and this method is used to identify the dynamic load on airfoil structure without and with considering random structure parameters. First of all, the newly proposed algorithm is proved to be efficient and convergent through the rigorous mathematics theory and the numerical results of determinate dynamic load identification. Secondly, using the perturbation method, we transform uncertain inverse problem about force reconstruction into determinate load identification problem. Lastly, the statistical characteristics of identified load are evaluated by statistical methods. Especially, this newly proposed approach has successfully solved determinate and uncertain inverse problems about dynamic load identification. Numerical simulations validate that the newly developed method in this paper is feasible and stable in solving load identification problems without and with considering random structure parameters. Additionally, it also shows that most of the observation error of the proposed algorithm in solving dynamic load identification of deterministic and random structure is respectively within 11.13%, 20%.

Variable selection and prediction performance of penalized two-part regression with community-based crime data application

  • Seong-Tae Kim;Man Sik Park
    • Communications for Statistical Applications and Methods
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    • 제31권4호
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    • pp.441-457
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    • 2024
  • Semicontinuous data are characterized by a mixture of a point probability mass at zero and a continuous distribution of positive values. This type of data is often modeled using a two-part model where the first part models the probability of dichotomous outcomes -zero or positive- and the second part models the distribution of positive values. Despite the two-part model's popularity, variable selection in this model has not been fully addressed, especially, in high dimensional data. The objective of this study is to investigate variable selection and prediction performance of penalized regression methods in two-part models. The performance of the selected techniques in the two-part model is evaluated via simulation studies. Our findings show that LASSO and ENET tend to select more predictors in the model than SCAD and MCP. Consequently, MCP and SCAD outperform LASSO and ENET for β-specificity, and LASSO and ENET perform better than MCP and SCAD with respect to the mean squared error. We find similar results when applying the penalized regression methods to the prediction of crime incidents using community-based data.

엑셀을 활용한 소그룹 모델링에서의 상호작용 -중학교 2학년 대수 영역을 중심으로- (Interactions in a Small Group Modeling Environment with Excel)

  • 류희찬;김지연
    • 대한수학교육학회지:수학교육학연구
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    • 제15권1호
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    • pp.75-105
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    • 2005
  • 본 연구는 엑셀을 활용한 소그룹 모델링의 흐름과 학생과 엑셀의 상호작용이 모델링에 미치는 영향에 대한 이해를 바탕으로 추후 엑셀을 활용한 소그룹 모델링을 통한 수학 교수ㆍ 학습을 위한 기초적인 정보를 제공하는데 목적이 있다. 엑셀을 활용한 소그룹 모델링의 흐름을 알아보기 위해 학생들이 고려하는 양, 양들간 관계, 구성하는 모델을 바탕으로 모델링 주기를 살펴보았다 또한 학생과 엑셀의 상호작용이 모델링에 미치는 영향을 이해하기 위해 학생과 엑셀의 상호작용을 모델 형성, 모델 정교화, 모델을 통한 상황 해석ㆍ예측ㆍ통제 측면에서 분석하였다. 본 연구로부터 엑셀을 활용한 소그룹 모델링이 어떻게 이루어지는가와 학생-엑셀 상호작용 패턴에 대한 이해를 바탕으로 모델링 도구로서의 엑셀의 잠재력을 확인하고 학생들의 모델링 활동에 있어서의 강점과 취약점을 확인할 수 있었다. 또한 엑셀을 활용한 소그룹 모델링이 보다 효과적으로 이루어지기 위해 요구되는 교사 역할에 관한 시사점을 얻을 수 있었다.

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