• Title/Summary/Keyword: 함수지도

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Interactive Statistics Laboratory using R and Sage (R을 활용한 '대화형 통계학 입문 실습실' 개발과 활용)

  • Lee, Sang-Gu;Lee, Geung-Hee;Choi, Yong-Seok;Lee, Jae Hwa;Lee, Jenny Jyoung
    • Communications of Mathematical Education
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    • v.29 no.4
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    • pp.573-588
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    • 2015
  • In this paper, we introduce development process and application of a simple and effective model of a statistics laboratory using open source software R, one of leading language and environment for statistical computing and graphics. This model consists of HTML files, including Sage cells, video lectures and enough internet resources. Users do not have to install statistical softwares to run their code. Clicking 'evaluate' button in the web page displays the result that is calculated through cloud-computing environment. Hence, with any type of mobile equipment and internet, learners can freely practice statistical concepts and theorems via various examples with sample R (or Sage) codes which were given, while instructors can easily design and modify it for his/her lectures, only gathering many existing resources and editing HTML file. This will be a resonable model of laboratory for studying statistics. This model with bunch of provided materials will reduce the time and effort needed for R-beginners to be acquainted with and understand R language and also stimulate beginners' interest in statistics. We introduce this interactive statistical laboratory as an useful model for beginners to learn basic statistical concepts and R.

A Study on Learning and Teaching Environments for Computers and Mathematics Education ('컴퓨터와 수학교육' 학습-지도 환경에 관한 연구)

  • Kim, Hwa-Kyung
    • Journal of Educational Research in Mathematics
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    • v.16 no.4
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    • pp.367-386
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    • 2006
  • There are two strands for considering tile relationships between education and technology. One is the viewpoint of 'learning from computers' and the other is that of 'learning with computers'. In this paper, we call mathematics education with computers as 'computers and mathematics education' and this computer environments as microworlds. In this paper, we first suggest theoretical backgrounds ai constructionism, mathematization, and computer interaction. These theoretical backgrounds are related to students, school mathematics and computers, relatively As specific strategies to design a microworld, we consider a physical construction, fuctiionization, and internet interaction. Next we survey the different microworlds such as Logo and Dynamic Geometry System(DGS), and reform each microworlds for mathematical level-up of representation. First, we introduce the concept of action letters and its manipulation for representing turtle actions and recursive patterns in turtle microworld. Also we introduce another algebraic representation for representing DGS relation and consider educational moaning in dynamic geometry microworld. We design an integrating microworld between Logo and DGS. First, we design a same command system and we get together in a microworld. Second, these microworlds interact each other and collaborate to construct and manipulate new objects such as tiles and folding nets.

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An empirical study for a better curriculum reform of statistical correlation based on an abduction (중등학교 상관관계 지도 내용 개선을 위한 가추적 실증 연구)

  • Lee, Young-Ha;Kim, So-Hyun
    • Journal of Educational Research in Mathematics
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    • v.22 no.3
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    • pp.371-386
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    • 2012
  • This research assumes two facts; One is that the mathematics curriculum reform of Korea in 2007 would have been better if it had been a revise instead of deletion and the other is that every school curriculum should be of help for the sound enhancement of all 6 types of logical concepts that appears in the Piaget's theory of cognitive development. What our mathematics curriculum has introduced as a correlation is not the one of the 6 logical concepts that Piaget had thought in his theory of cognitive development. In order to see the reason of that difference, we check the difference of jargons among the academic denominations, such as Pedagogy, Psychology and Statistics through their college textbooks. Because we suppose that the mismatch of 'Piaget's vs Curriculum's correlation' is due to the mis-communication among scholars of different academic denominations. With what we learned via the above analytical study leaned on an abduction and to get some idea on them for the potential future construction of school Statistics curriculum when it should be returned, which we believe so, we observe two foreign highschool mathematics textbooks briefly. As a result of the study, we found that the concept of correlation in Pedagogy contain all kinds of relation while it was stingy in Statistics. Here we report a main result; A careful discretion among similar concepts of correlation, such as linear relationship(correlation), stochastic change along conditions(dependence), central comparison(other relation) are needed for the potential future curriculum. And if new curriculum contains the linear correlation then we strongly recommend to involve the regression line to connect it with the linear function chapter.

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Blind Adaptive Equalization of Partial Response Channels (부분 응답 채널에서의 블라인드 적응 등화 기술에 관한 연구)

  • 이상경;이재천
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.26 no.11A
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    • pp.1827-1840
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    • 2001
  • In digital data transmission/storage systems, the compensation for channel distortion is conducted normally using a training sequence that is known a priori to both the sender and receiver. The use of the training sequences results in inefficient utilization of channel bandwidth. Sometimes, it is also impossible to send training sequences such as in the burst-mode communication. As such, a great deal of attention has been given to the approach requiring no training sequences, which has been called the blind equalization technique. On the other hand, to utilize the limited bandwidth effectively, the concept of partial response (PR) signaling has widely been adopted in both the high-speed transmission and high-density recording/playback systems such as digital microwave, digital subscriber loops, hard disk drives, digital VCRs and digital versatile recordable disks and so on. This paper is concerned with blind adaptive equalization of partial response channels whose transfer function zeros are located on the unit circle, thereby causing some problems in performance. Specifically we study how the problems of blind channel equalization associated with the PR channels can be improved. In doing so, we first discuss the existing methods and then propose new structures for blind PR channel equalization. Our structures have been extensively tested by computer simulation and found out to be encouraging in performance. The results seem very promising as well in terms of the implementation complexity compared to the previous approach reported in literature.

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Review of Dam-Reservoir water level considering Dam-downstream situation (직하류 하천환경을 고려한 댐 저수량 수위 확보 검토)

  • Kim, Chang-soon;Kim, Jong-Rae
    • Proceedings of the Korea Water Resources Association Conference
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    • 2017.05a
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    • pp.377-377
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    • 2017
  • 다목적댐은 비어있는 저수지 용량을 활용, 상류에서 유입되는 홍수를 저류하여 하류의 피해를 경감시키고, 저류된 저수량을 활용하여 갈수시 생 공 유지용수 등을 목적에 맞게 하류로의 공급에 주요 목적이 있다. 이를 위해 댐 계획에는 상류에서 유입되는 목표 빈도 계획홍수량을 산정하고, 이에 따른 여수로의 계획방류량 등이 포함된 홍수 조절 방안이 수립된다. 다목적댐은 그 중요도 때문에 많은 사회적 재화(財貨)가 투입되어 하천에서 가장 높은 빈도인 200년 빈도 홍수량에 대비하도록 설계되어 있다. 그러나 대부분의 댐 하류 하천에서는 긴 연장에 따른 투자비용 등의 한계로 상류 댐에 미치지 못하는 100년 빈도 이하로 설정되어있다. 이런 상 하류의 홍수계획간 괴리로 댐의 계획 방류량 수준의 홍수 조절시에는 하류 하천에 재난상황으로 발생할 우려가 있다. 기상예보의 고도화로 단기 예보의 정밀도가 높아져 단기간 댐 운영에는 효과적으로 활용되고 있다. 하지만 5일 이후를 예보하는 중 장기예보는 아직까지도 불확실성이 높은 실정이다. 여기에 기후변화 등 기상의 불확실성을 고려하여 홍수기 초 장마와 태풍 등의 영향에 대비하기 위해 무작정 댐을 저(低)수위로 운영하면 이후 여름 가뭄에 취약해 지고, 반대로 저수량 확보의 고(高)수위 운영을 할 경우 연이은 태풍 등 홍수상황에 취약해 지게 된다. 최근 '14~'15년도 낙동강 수계에 여름가뭄으로 안동 임하댐이 가뭄단계에 돌입하는 등 홍수기초 적정 저수량의 확보는 안정적 수자원시설 운영에 중요성이 커지고 있다. 본 연구에서는 이러한 불확실한 기상상황에 대비하고 댐의 이치수 목적 달성을 위해, 홍수기초 가능한 저수량을 확보하되 계획홍수량이 들어와도 하류피해는 경감시킬 수 있는 저수지 수위를 찾고자하였다. 이를 위해 낙동강 수계 9개 다목적댐(안동, 임하, 성덕, 보현산, 군위, 김천부항, 합천, 남강, 밀양댐)을 대상으로 댐 설계 및 직하류 하천 상황을 고려한 "홍수기초 댐 저수량 확보 수위 검토"를 실시하였다. 댐 직하류 하천의 홍수대비 상황 및 홍수조절시 제약사항 등을 조사해 주요지점(Critical Point)을 선정하고 그 지점의 홍수량을 파악한다. 이어서 저류함수 모형을 활용하여 댐별 저수지 모의 운영을 실시하였다. 대상 댐 저수지에 계획홍수량을 유입시키고 수위를 점차 조정하면서 하류 지점의 홍수량 내의 규모로 방류를 하는 저수지 모의 운영을 실시하였다. 이때 저수지의 계획홍수위를 초과하지 않는 등 안정적 홍수조절이 가능한 특정 수위를 찾아 하류 하천 환경을 고려한 댐 운영 수위로 선정하였다. 최근 홍수기총에는 강수량이 계속 줄어들고 홍수기 이후 더 많은 강수가 내리는 등 기후변화로 댐 운영은 날로 어려워지고 있다. 본 연구의 분석 결과는 홍수기초 가뭄 및 장마 또는 태풍 등에 대비하여 댐 운영의 이 치수 두 가지 목적을 달성하는데 참고가 될 수 있을 것이다.

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A Study of CHAMP Satellite Magnetic Anomalies in East Asia (동아시아지역에서의 CHAMP 위성자료에서의 지각 자기이상의 연구)

  • Kim, Hyung Rae
    • Economic and Environmental Geology
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    • v.54 no.1
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    • pp.117-126
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    • 2021
  • Satellite magnetic observations reflect the magnetic properties of deep crust about the depth of Curie isotherm that is a boundary where the magnetic nature of the rocks is disappeared, showing long wavelength anomalies that are not easily detected in near-surface data from airborne and shipborne surveys. For this reason, they are important not only in the analyses on such as plate reconstruction of tectonic boundaries and deep crustal structures, but in the studies of geothermal distribution in Antarctic and Greenland crust, related to global warming issue. It is a conventional method to compute the spherical harmonic coefficients from global coverage of satellite magnetic observations but it should be noted that inclusion of erroneous data from the equator and the poles where magnetic observations are highly disturbed might mislead the global model of the coefficients. Otherwise, the reduced anomaly model can be obtained with less corruption by choosing the area of interest with proper data processing to the area. In this study, I produced a satellite crustal magnetic anomaly map over East Asia (20° ~ 55°N, 108° ~ 150°E) centered on Korean Peninsula, from CHAMP satellite magnetic measurements about mean altitude of 280 km during the last year of the mission, and compared with the one from global crustal magnetic model (MF7). Also, a comparison was made with long wavelength anomalies from EMAG2 model compiled from all near-surface data over the globe.

Water temperature prediction of Daecheong Reservoir by a process-guided deep learning model (역학적 모델과 딥러닝 모델을 융합한 대청호 수온 예측)

  • Kim, Sung Jin;Park, Hyungseok;Lee, Gun Ho;Chung, Se Woong
    • Proceedings of the Korea Water Resources Association Conference
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    • 2021.06a
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    • pp.88-88
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    • 2021
  • 최근 수자원과 수질관리 분야에 자료기반 머신러닝 모델과 딥러닝 모델의 활용이 급증하고 있다. 그러나 딥러닝 모델은 Blackbox 모델의 특성상 고전적인 질량, 운동량, 에너지 보존법칙을 고려하지 않고, 데이터에 내재된 패턴과 관계를 해석하기 때문에 물리적 법칙을 만족하지 않는 예측결과를 가져올 수 있다. 또한, 딥러닝 모델의 예측 성능은 학습데이터의 양과 변수 선정에 크게 영향을 받는 모델이기 때문에 양질의 데이터가 제공되지 않으면 모델의 bias와 variation이 클 수 있으며 정확도 높은 예측이 어렵다. 최근 이러한 자료기반 모델링 방법의 단점을 보완하기 위해 프로세스 기반 수치모델과 딥러닝 모델을 결합하여 두 모델링 방법의 장점을 활용하는 연구가 활발히 진행되고 있다(Read et al., 2019). Process-Guided Deep Learning (PGDL) 방법은 물리적 법칙을 반영하여 딥러닝 모델을 훈련시킴으로써 순수한 딥러닝 모델의 물리적 법칙 결여성 문제를 해결할 수 있는 대안으로 활용되고 있다. PGDL 모델은 딥러닝 모델에 물리적인 법칙을 해석할 수 있는 추가변수를 도입하며, 딥러닝 모델의 매개변수 최적화 과정에서 Cost 함수에 물리적 법칙을 위반하는 경우 Penalty를 추가하는 알고리즘을 도입하여 물리적 보존법칙을 만족하도록 모델을 훈련시킨다. 본 연구의 목적은 대청호의 수심별 수온을 예측하기 위해 역학적 모델과 딥러닝 모델을 융합한 PGDL 모델을 개발하고 적용성을 평가하는데 있다. 역학적 모델은 2차원 횡방향 평균 수리·수질 모델인 CE-QUAL-W2을 사용하였으며, 대청호를 대상으로 2017년부터 2018년까지 총 2년간 수온과 에너지 수지를 모의하였다. 기상(기온, 이슬점온도, 풍향, 풍속, 운량), 수문(저수위, 유입·유출 유량), 수온자료를 수집하여 CE-QUAL-W2 모델을 구축하고 보정하였으며, 모델은 저수위 변화, 수온의 수심별 시계열 변동 특성을 적절하게 재현하였다. 또한, 동일기간 대청호 수심별 수온 예측을 위한 순환 신경망 모델인 LSTM(Long Short-Term Memory)을 개발하였으며, 종속변수는 수온계 체인을 통해 수집한 수심별 고빈도 수온 자료를 사용하고 독립 변수는 기온, 풍속, 상대습도, 강수량, 단파복사에너지, 장파복사에너지를 사용하였다. LSTM 모델의 매개변수 최적화는 지도학습을 통해 예측값과 실측값의 RMSE가 최소화 되로록 훈련하였다. PGDL 모델은 동일 기간 LSTM 모델과 동일 입력 자료를 사용하여 구축하였으며, 역학적 모델에서 얻은 에너지 수지를 만족하지 않는 경우 Cost Function에 Penalty를 추가하여 물리적 보존법칙을 만족하도록 훈련하고 수심별 수온 예측결과를 비교·분석하였다.

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A Study on Teaching the Method of Lagrange Multipliers in the Era of Digital Transformation (라그랑주 승수법의 교수·학습에 대한 소고: 라그랑주 승수법을 활용한 주성분 분석 사례)

  • Lee, Sang-Gu;Nam, Yun;Lee, Jae Hwa
    • Communications of Mathematical Education
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    • v.37 no.1
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    • pp.65-84
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    • 2023
  • The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

Anomaly Detection for User Action with Generative Adversarial Networks (적대적 생성 모델을 활용한 사용자 행위 이상 탐지 방법)

  • Choi, Nam woong;Kim, Wooju
    • Journal of Intelligence and Information Systems
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    • v.25 no.3
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    • pp.43-62
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    • 2019
  • At one time, the anomaly detection sector dominated the method of determining whether there was an abnormality based on the statistics derived from specific data. This methodology was possible because the dimension of the data was simple in the past, so the classical statistical method could work effectively. However, as the characteristics of data have changed complexly in the era of big data, it has become more difficult to accurately analyze and predict the data that occurs throughout the industry in the conventional way. Therefore, SVM and Decision Tree based supervised learning algorithms were used. However, there is peculiarity that supervised learning based model can only accurately predict the test data, when the number of classes is equal to the number of normal classes and most of the data generated in the industry has unbalanced data class. Therefore, the predicted results are not always valid when supervised learning model is applied. In order to overcome these drawbacks, many studies now use the unsupervised learning-based model that is not influenced by class distribution, such as autoencoder or generative adversarial networks. In this paper, we propose a method to detect anomalies using generative adversarial networks. AnoGAN, introduced in the study of Thomas et al (2017), is a classification model that performs abnormal detection of medical images. It was composed of a Convolution Neural Net and was used in the field of detection. On the other hand, sequencing data abnormality detection using generative adversarial network is a lack of research papers compared to image data. Of course, in Li et al (2018), a study by Li et al (LSTM), a type of recurrent neural network, has proposed a model to classify the abnormities of numerical sequence data, but it has not been used for categorical sequence data, as well as feature matching method applied by salans et al.(2016). So it suggests that there are a number of studies to be tried on in the ideal classification of sequence data through a generative adversarial Network. In order to learn the sequence data, the structure of the generative adversarial networks is composed of LSTM, and the 2 stacked-LSTM of the generator is composed of 32-dim hidden unit layers and 64-dim hidden unit layers. The LSTM of the discriminator consists of 64-dim hidden unit layer were used. In the process of deriving abnormal scores from existing paper of Anomaly Detection for Sequence data, entropy values of probability of actual data are used in the process of deriving abnormal scores. but in this paper, as mentioned earlier, abnormal scores have been derived by using feature matching techniques. In addition, the process of optimizing latent variables was designed with LSTM to improve model performance. The modified form of generative adversarial model was more accurate in all experiments than the autoencoder in terms of precision and was approximately 7% higher in accuracy. In terms of Robustness, Generative adversarial networks also performed better than autoencoder. Because generative adversarial networks can learn data distribution from real categorical sequence data, Unaffected by a single normal data. But autoencoder is not. Result of Robustness test showed that he accuracy of the autocoder was 92%, the accuracy of the hostile neural network was 96%, and in terms of sensitivity, the autocoder was 40% and the hostile neural network was 51%. In this paper, experiments have also been conducted to show how much performance changes due to differences in the optimization structure of potential variables. As a result, the level of 1% was improved in terms of sensitivity. These results suggest that it presented a new perspective on optimizing latent variable that were relatively insignificant.

The Equilibrium Moisture Content - Relative Humidity Relationship of Tropical Woods (관계습도(關係濕度)와 목재(木材)의 평형함수량(平衡含水量)과의 관계(關係)에 대(對)한 연구(硏究))

  • Shim, Chong-Supp
    • Journal of the Korean Wood Science and Technology
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    • v.10 no.3
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    • pp.4-12
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    • 1982
  • 1. Under the request of the Dept. of Navy, U.S.A. this investigation has been done as a part work of the Navy Research Project of Tropical Woods at the Wood Technology Laboratory, School of Forestry, Yale University, New Haven, Conn., U.S.A. 2. In order to determine the equilibrium moisture content and hysteresis loop of three tropical woods (Ocotea, Tablebuia, and Hymenaea) which have not been tested the physical properties, this investigation has made with small thin specimens (1.5"${\times}$1.0${\times}$0.4) under four different controlled relative humidity conditions (that is, 21%, 53%, 60%, and 83%). 3. As the result, the equilibrium moisture content and hysteresis loop of three tropical woods have been shown in the Table and Figures 2, 3 and 4. 4. According to the results, it is concluded that there are the considerable differences in the equilibrium moisture content under the same relative humidity condition and the type of hysteresis loop between different species which have been tested. 5. Desorption of lumber with slightly oscillating humidity of each species tested, has shown on the Table 9 and it has almost the same tendency of results showing the difference between species as the small specimen. 6. Although it is hard to compare the difference of results, E.M.C., and hysteresis between tropical wood and woods from temperate zone, there are, however, still some difference between species. 7. The author wishes to acknowledge my indebtedness to Prof. Wangaard, and Prof. Dickinson for the competent guidance and good advice on this study, and also to Mr. Clanchs for the help in getting materials for the experiment.

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