• Title/Summary/Keyword: Dynamic Learning

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Investigating Dynamic Mutation Process of Issues Using Unstructured Text Analysis (부도예측을 위한 KNN 앙상블 모형의 동시 최적화)

  • Min, Sung-Hwan
    • Journal of Intelligence and Information Systems
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    • v.22 no.1
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    • pp.139-157
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    • 2016
  • Bankruptcy involves considerable costs, so it can have significant effects on a country's economy. Thus, bankruptcy prediction is an important issue. Over the past several decades, many researchers have addressed topics associated with bankruptcy prediction. Early research on bankruptcy prediction employed conventional statistical methods such as univariate analysis, discriminant analysis, multiple regression, and logistic regression. Later on, many studies began utilizing artificial intelligence techniques such as inductive learning, neural networks, and case-based reasoning. Currently, ensemble models are being utilized to enhance the accuracy of bankruptcy prediction. Ensemble classification involves combining multiple classifiers to obtain more accurate predictions than those obtained using individual models. Ensemble learning techniques are known to be very useful for improving the generalization ability of the classifier. Base classifiers in the ensemble must be as accurate and diverse as possible in order to enhance the generalization ability of an ensemble model. Commonly used methods for constructing ensemble classifiers include bagging, boosting, and random subspace. The random subspace method selects a random feature subset for each classifier from the original feature space to diversify the base classifiers of an ensemble. Each ensemble member is trained by a randomly chosen feature subspace from the original feature set, and predictions from each ensemble member are combined by an aggregation method. The k-nearest neighbors (KNN) classifier is robust with respect to variations in the dataset but is very sensitive to changes in the feature space. For this reason, KNN is a good classifier for the random subspace method. The KNN random subspace ensemble model has been shown to be very effective for improving an individual KNN model. The k parameter of KNN base classifiers and selected feature subsets for base classifiers play an important role in determining the performance of the KNN ensemble model. However, few studies have focused on optimizing the k parameter and feature subsets of base classifiers in the ensemble. This study proposed a new ensemble method that improves upon the performance KNN ensemble model by optimizing both k parameters and feature subsets of base classifiers. A genetic algorithm was used to optimize the KNN ensemble model and improve the prediction accuracy of the ensemble model. The proposed model was applied to a bankruptcy prediction problem by using a real dataset from Korean companies. The research data included 1800 externally non-audited firms that filed for bankruptcy (900 cases) or non-bankruptcy (900 cases). Initially, the dataset consisted of 134 financial ratios. Prior to the experiments, 75 financial ratios were selected based on an independent sample t-test of each financial ratio as an input variable and bankruptcy or non-bankruptcy as an output variable. Of these, 24 financial ratios were selected by using a logistic regression backward feature selection method. The complete dataset was separated into two parts: training and validation. The training dataset was further divided into two portions: one for the training model and the other to avoid overfitting. The prediction accuracy against this dataset was used to determine the fitness value in order to avoid overfitting. The validation dataset was used to evaluate the effectiveness of the final model. A 10-fold cross-validation was implemented to compare the performances of the proposed model and other models. To evaluate the effectiveness of the proposed model, the classification accuracy of the proposed model was compared with that of other models. The Q-statistic values and average classification accuracies of base classifiers were investigated. The experimental results showed that the proposed model outperformed other models, such as the single model and random subspace ensemble model.

The Development and Effectiveness of a PBL Based Career Education Program (PBL 기반 진로교육 프로그램의 개발 및 효과검증)

  • Lee, Hye-Suk;Kim, You-Me
    • The Korean Journal of Elementary Counseling
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    • v.8 no.1
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    • pp.33-50
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    • 2009
  • The purpose of this study was to develop a PBL-based career education program and to examine its effectiveness on school children's career maturity. It's specifically meant to prepare a career education program to assist students to get an accurate grip on their aptitude, interest and personality and explore various sorts of occupations in the course of solving authentic and contextual career-related problems. After children's developmental characteristics and needs were analyzed, task analysis was implemented, and the objectives were defined. And then the core of the program, PBL problems were developed, and the validity of the problems were verified Evaluation plans and tools were prepared to assess children's problem-solving process and presentation, and an online learning space was designed. The program that consisted of 10-minute 21 sessions was provided to fifth-grade elementary schoolers for eight weeks. The findings of the study were as follows: The experimental group that participated in the PBL-based career education program showed a more significant improvement than the control group that didn't in career attitude and three career attitude subfactors involving planness, disposition and compromise. And the former made a more significant progress than the latter in career ability and its subfactors including vocational comprehension, self-understanding and decision-making skills as well. As a result of making a content analysis to make up for the survey, the students reported that they were able to get an objective understanding of themselves and acquire diverse and profound knowledge on work and the business world in the middle of solving the given PBL problems related to different areas in group and giving a presentation. In conclusion, a PBL based career education program developed by this researcher encouraged the students to have an objective self-understanding, to have a dynamic interactive discussion with their group members. Therefore the program had a positive impact on boosting the career attitude and career ability of the elementary schoolers. The findings suggested that in the field of elementary career education, autonomous learning attitude and subjecthood are the crucial factors to stimulate school children to explore and create their own future.

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Context Prediction Using Right and Wrong Patterns to Improve Sequential Matching Performance for More Accurate Dynamic Context-Aware Recommendation (보다 정확한 동적 상황인식 추천을 위해 정확 및 오류 패턴을 활용하여 순차적 매칭 성능이 개선된 상황 예측 방법)

  • Kwon, Oh-Byung
    • Asia pacific journal of information systems
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    • v.19 no.3
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    • pp.51-67
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    • 2009
  • Developing an agile recommender system for nomadic users has been regarded as a promising application in mobile and ubiquitous settings. To increase the quality of personalized recommendation in terms of accuracy and elapsed time, estimating future context of the user in a correct way is highly crucial. Traditionally, time series analysis and Makovian process have been adopted for such forecasting. However, these methods are not adequate in predicting context data, only because most of context data are represented as nominal scale. To resolve these limitations, the alignment-prediction algorithm has been suggested for context prediction, especially for future context from the low-level context. Recently, an ontological approach has been proposed for guided context prediction without context history. However, due to variety of context information, acquiring sufficient context prediction knowledge a priori is not easy in most of service domains. Hence, the purpose of this paper is to propose a novel context prediction methodology, which does not require a priori knowledge, and to increase accuracy and decrease elapsed time for service response. To do so, we have newly developed pattern-based context prediction approach. First of ail, a set of individual rules is derived from each context attribute using context history. Then a pattern consisted of results from reasoning individual rules, is developed for pattern learning. If at least one context property matches, say R, then regard the pattern as right. If the pattern is new, add right pattern, set the value of mismatched properties = 0, freq = 1 and w(R, 1). Otherwise, increase the frequency of the matched right pattern by 1 and then set w(R,freq). After finishing training, if the frequency is greater than a threshold value, then save the right pattern in knowledge base. On the other hand, if at least one context property matches, say W, then regard the pattern as wrong. If the pattern is new, modify the result into wrong answer, add right pattern, and set frequency to 1 and w(W, 1). Or, increase the matched wrong pattern's frequency by 1 and then set w(W, freq). After finishing training, if the frequency value is greater than a threshold level, then save the wrong pattern on the knowledge basis. Then, context prediction is performed with combinatorial rules as follows: first, identify current context. Second, find matched patterns from right patterns. If there is no pattern matched, then find a matching pattern from wrong patterns. If a matching pattern is not found, then choose one context property whose predictability is higher than that of any other properties. To show the feasibility of the methodology proposed in this paper, we collected actual context history from the travelers who had visited the largest amusement park in Korea. As a result, 400 context records were collected in 2009. Then we randomly selected 70% of the records as training data. The rest were selected as testing data. To examine the performance of the methodology, prediction accuracy and elapsed time were chosen as measures. We compared the performance with case-based reasoning and voting methods. Through a simulation test, we conclude that our methodology is clearly better than CBR and voting methods in terms of accuracy and elapsed time. This shows that the methodology is relatively valid and scalable. As a second round of the experiment, we compared a full model to a partial model. A full model indicates that right and wrong patterns are used for reasoning the future context. On the other hand, a partial model means that the reasoning is performed only with right patterns, which is generally adopted in the legacy alignment-prediction method. It turned out that a full model is better than a partial model in terms of the accuracy while partial model is better when considering elapsed time. As a last experiment, we took into our consideration potential privacy problems that might arise among the users. To mediate such concern, we excluded such context properties as date of tour and user profiles such as gender and age. The outcome shows that preserving privacy is endurable. Contributions of this paper are as follows: First, academically, we have improved sequential matching methods to predict accuracy and service time by considering individual rules of each context property and learning from wrong patterns. Second, the proposed method is found to be quite effective for privacy preserving applications, which are frequently required by B2C context-aware services; the privacy preserving system applying the proposed method successfully can also decrease elapsed time. Hence, the method is very practical in establishing privacy preserving context-aware services. Our future research issues taking into account some limitations in this paper can be summarized as follows. First, user acceptance or usability will be tested with actual users in order to prove the value of the prototype system. Second, we will apply the proposed method to more general application domains as this paper focused on tourism in amusement park.

Comparative Assessment of Linear Regression and Machine Learning for Analyzing the Spatial Distribution of Ground-level NO2 Concentrations: A Case Study for Seoul, Korea (서울 지역 지상 NO2 농도 공간 분포 분석을 위한 회귀 모델 및 기계학습 기법 비교)

  • Kang, Eunjin;Yoo, Cheolhee;Shin, Yeji;Cho, Dongjin;Im, Jungho
    • Korean Journal of Remote Sensing
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    • v.37 no.6_1
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    • pp.1739-1756
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    • 2021
  • Atmospheric nitrogen dioxide (NO2) is mainly caused by anthropogenic emissions. It contributes to the formation of secondary pollutants and ozone through chemical reactions, and adversely affects human health. Although ground stations to monitor NO2 concentrations in real time are operated in Korea, they have a limitation that it is difficult to analyze the spatial distribution of NO2 concentrations, especially over the areas with no stations. Therefore, this study conducted a comparative experiment of spatial interpolation of NO2 concentrations based on two linear-regression methods(i.e., multi linear regression (MLR), and regression kriging (RK)), and two machine learning approaches (i.e., random forest (RF), and support vector regression (SVR)) for the year of 2020. Four approaches were compared using leave-one-out-cross validation (LOOCV). The daily LOOCV results showed that MLR, RK, and SVR produced the average daily index of agreement (IOA) of 0.57, which was higher than that of RF (0.50). The average daily normalized root mean square error of RK was 0.9483%, which was slightly lower than those of the other models. MLR, RK and SVR showed similar seasonal distribution patterns, and the dynamic range of the resultant NO2 concentrations from these three models was similar while that from RF was relatively small. The multivariate linear regression approaches are expected to be a promising method for spatial interpolation of ground-level NO2 concentrations and other parameters in urban areas.

A Study on the Garden Culture and Ideology based on the Confucianism and Taoism of the Song Dynasty - Focused on Zhū Xī(朱熹) and Báiyùchán(白玉蟾) - (송대(宋代) 유가와 도교에 근거한 원림 문화와 사상 고찰 - 주희(朱熹)와 백옥섬(白玉蟾)을 중심으로 -)

  • Park So-Hyun
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.41 no.1
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    • pp.10-20
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    • 2023
  • Zhū Xī, the representative of Confucianism, and Báiyùchán, the representative of Taoism in the South Song Dynasty, showed different sense of appreciation and enjoyment on the same space that was Mountain Wǔyí in their ideologically cultural ways. Based on the temples Wŭyíjīngshè(武夷精舍) where Zhū Xī stayed and Zhĭzhĭān(止止庵) where Báiyùchán resided, this study revealed their lives in such temples to look into their appreciation on ideology and space. Then, based on the words 'YiBoEumYeong [移步吟詠]' shown on the poetry they chanted in relation with Wǔyíjiǔqū from its 1st valley to its 9th valley, this study examines their understanding of scenery and system of appreciation that appeared in dynamic ways to conclude: First, even same scenery shows different understanding of scenery and appreciation of space in accordance with the viewers' thinking ways of culture. Second, as the Confucianism and Taoism influenced in ideologically cultural ways to develop each other in the Song dynasty, they absorbed their merits each other to supplement shortcomings in their own. In this process, they made it clear that their own propositions were different between them in their essential meanings although they used common terms for such propositions. Third, as the Confucian master who compiled the Neo-Confucianism of the South Song dynasty, Zhū Xī regarded Wŭyíjīngshè and Wǔyíjiǔqū as a place of learning and a place of seeking the truth to go for 'being unified with nature' so that everyday life can be united with Tao of Li [理] everywhere beyond the limited appreciation of the scenery. That is, this thought works for 'recovery of nature of our own [復其性]', the learning goal of Confucianism, and is aimed to 'cultivate the essential nature of our own(性情涵養)' through such beautiful nature. Fourth, as the master of Keumdan family of the South Song Taoism, Báiyùchán regarded Zhĭzhĭān and Wǔyíjiǔqū as a Taoist temple that has a long history rooting from Taesangwon temple, a clean place of discipline to become a Taoist hermit through hard training. He, therefore, directly referred to Zhĭzhĭān and Wǔyíjiǔqū in relation with the Taoist legends remaining in Wǔyíjiǔqū such as hermits' dinners, female hermits, leaving the human world as a hermit and so on as ways for becoming a hermit so that he went for the level of perfectly going out of human world and becoming a hermit. He, therefore, defined Mountain Wǔyí as a world and universe of hermits where he himself too hovered between outside and inside of poetry literature as a hermit through the mood and attitude of keeping himself enjoying the scenery as a hermit.

A New Bias Scheduling Method for Improving Both Classification Performance and Precision on the Classification and Regression Problems (분류 및 회귀문제에서의 분류 성능과 정확도를 동시에 향상시키기 위한 새로운 바이어스 스케줄링 방법)

  • Kim Eun-Mi;Park Seong-Mi;Kim Kwang-Hee;Lee Bae-Ho
    • Journal of KIISE:Software and Applications
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    • v.32 no.11
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    • pp.1021-1028
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    • 2005
  • The general solution for classification and regression problems can be found by matching and modifying matrices with the information in real world and then these matrices are teaming in neural networks. This paper treats primary space as a real world, and dual space that Primary space matches matrices using kernel. In practical study, there are two kinds of problems, complete system which can get an answer using inverse matrix and ill-posed system or singular system which cannot get an answer directly from inverse of the given matrix. Further more the problems are often given by the latter condition; therefore, it is necessary to find regularization parameter to change ill-posed or singular problems into complete system. This paper compares each performance under both classification and regression problems among GCV, L-Curve, which are well known for getting regularization parameter, and kernel methods. Both GCV and L-Curve have excellent performance to get regularization parameters, and the performances are similar although they show little bit different results from the different condition of problems. However, these methods are two-step solution because both have to calculate the regularization parameters to solve given problems, and then those problems can be applied to other solving methods. Compared with UV and L-Curve, kernel methods are one-step solution which is simultaneously teaming a regularization parameter within the teaming process of pattern weights. This paper also suggests dynamic momentum which is leaning under the limited proportional condition between learning epoch and the performance of given problems to increase performance and precision for regularization. Finally, this paper shows the results that suggested solution can get better or equivalent results compared with GCV and L-Curve through the experiments using Iris data which are used to consider standard data in classification, Gaussian data which are typical data for singular system, and Shaw data which is an one-dimension image restoration problems.

A Study on Yulgok School Scholars' Theory to Study "Daehak(大學, Great Learning)"-Focusing on Horon(湖論) and Nakron(洛論) Scholars' Opinions of Bunyeom(浮念) and Pyeonnyeom(偏念) (율곡학파 학자들의 『대학』 공부론 연구- 부념(浮念)과 편념(偏念)에 관한 호론과 낙론 학자들의 견해를 중심으로 -)

  • 정연수
    • 유학연구
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    • v.47
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    • pp.43-66
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    • 2019
  • In this thesis, based on Yulgok's theory to study "Daehak", it was examined how scholars of Horn and Nakron developed the theory to study "Daehak" regarding Bunyeom and Pyeonnyeom in the context of the history of ideas. The scholars of Horon and Nakron developed Yulgok's theory to study "Daehak" arguing that one could fully recover a saint's mind only after studying Seongeui(誠意, sincerity) to get rid of Aknyeom(惡念, an evil intention), Jeongsim(正心, an upright heart) to control Bunyeom, and Susin(修身, moral training) to control study and Pyeonnyeom. Yet, as scholars of Nakron criticized Horon scholars' argument considering the study of Jeongsim to control Bunyeom as Jeongsi(靜時, calm time), the controversy over the theory to study "Daehak" developed. The scholars of Horon generally insisted that because the method of Seongchal(省察, introspection) suggested in "Jeongsimjang(正心章, Chapter of Upright Heart)" of "Daehak" was not going into Dongsi(動時, dynamic time) and fathoming with Saryeo(思慮, consideration), but releasing it at the very moment of catching the indication of four troubles relevant to Bunyeom, the study on Jeongsim in "Daehak" should be the study of Jeongsi(靜時, calm time) for Jonyang(存養, developing good nature) of the main part of mind. On the other hand, the scholars of Nakron mostly contended that because Sim(心, mind) discussed in "Jeongsimjang" of "Daehak" referred to the whole mind and was not limited to Mibalsim(未發心, mind not manifested yet) of Jeongsi(靜時, calm time), the study on Jeongsim should include Dongjeong(動靜, movements). Yulgok once commented on Lee Yeon-pyeong(李延平)'s study on Mi-bal-che-in(未發體 認) in the same context of the study methods of release at the very moment of light reflection(輕輕照管·輕輕放退). In this respect, study on Jeongsim to control Bunyeom can be separated and belong to the study on Mibal of Jeongsi(靜時, calm time) as the scholars of Horon did. On the other hand, from the aspect that regarding the study on Jeongsim, Yulgok discussed both Jonyang(存養, developing good nature) and Seongchal(省察, introspection) with Mibal(未發, not manifested) and Yibal(已發, already manifested) together, it seems to have no problem to think of Jeongsim as the study including Dongjeong(動靜, movements). There were no different opinions between the scholars of Horon and those of Nakron regarding that there was study of Jeongsi(靜時, calm time) in "Daehak", too. However, while the scholars of Horon usually understood the study of Jeongsim in "Daehak" itself as the study of Mibal in "Jungyong", some scholars of Nakron thought that even though the study of Jeongsim of "Daehak" corresponded to Dongsi(動時, dynamic time), it included the study on Mibal because of the logic of Che-yong-il-won(體用一源). It can be said that the discussion over the study of Jeongsim to control Bunyeom and the study of Susin to control Pyeonnyeom were not limited to the proposal of the methodology to just control Bunyeom and Pyeonnyeom, but developed into the understanding of "Daehak" and "Jungyong" as one system of study.

The application of photographs resources for constructive social studies (구성주의적 사회과 교육을 위한 사진자료 활용방안)

  • Lee, Ki-Bok;Hwang, Hong-Seop
    • Journal of the Korean association of regional geographers
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    • v.6 no.3
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    • pp.117-138
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    • 2000
  • This study is, from the view point of constructive social studies which is the foundation of the 7th curriculum, to explore whether there is any viable program and to investigate it by which students, using photo resources in social studies, can organize their knowledge in the way of self-directed thinking. The main results are as follows: If it is a principle of knowledge construction process of constructive social studies that individual construction (cognitive construction) develops into communal construction(social construction) and yet communal construction develops itself, interacting with individual construction, it will be meet the objectives of social studies. In social studies, photos are a powerful communication tool. communicating with photos enables to invoke not only the visual aspects but also invisible aspects of social phenomena from photos. It, therefore, can help develop thinking power through inquiry learning, which is one of the emphasis of the 7th curriculum. Having analyzed photo resources appeared on the regional textbooks in elementary social studies, they have been appeared that even though the importance and amount of space photo resources occupy per page is big with regard to total resources, most of the photos failed to lad to self-directed thinking but just assistant material in stead. Besides, there appeared some problems with the title, variety, size, position, tone of color, visibility of the photos, and further with the combination of the photos. Developing of photo resources for constructive social studies is to overcome some problems inherent in current text books and to reflect the theoretical background of the 7th curriculum. To develop the sort of photo that can realize the point just mentioned, it would be highly preferable to provide photo database to facilitate study with homepage through web-based interaction. To take advantage of constructive photo resources, the instruction is strategized in four stages, intuition, conflict, accommodation, and equilibration stage. With the advancement of the era of image culture, curriculum developers are required to develop dynamic, multidimensional digital photos rather than static photos when develop text books.

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Evaluation of Endothelium-dependent Myocardial Perfusion Reserve in Healthy Smokers; Cold Pressor Test using $H_2^{15}O\;PET$ (흡연자에서 관상동맥 내피세포 의존성 심근 혈류 예비능: $H_2^{15}O\;PET$ 찬물자극 검사에 의한 평가)

  • Hwang, Kyung-Hoon;Lee, Dong-Soo;Lee, Byeong-Il;Lee, Jae-Sung;Lee, Ho-Young;Chung, June-Key;Lee, Myung-Chul
    • The Korean Journal of Nuclear Medicine
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    • v.38 no.1
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    • pp.21-29
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    • 2004
  • Purpose: Much evidence suggests long-term cigarette smoking alters coronary vascular endothelial response. On this study, we applied nonnegative matrix factorization (NMF), an unsupervised learning algorithm, to CO-less $H_2^{15}O-PET$ to investigate coronary endothelial dysfunction caused by smoking noninvasively. Materials and methods: This study enrolled eighteen young male volunteers consisting of 9 smokers $(23.8{\pm}1.1\;yr;\;6.5{\pm}2.5$ pack-years) and 9 nonsmokers $(23.8{\pm}2.9 yr)$. They do not have any cardiovascular risk factor or disease history. Myocardial $H_2^{15}O-PET$ was performed at rest, during cold ($5^{\circ}C$) pressor stimulation and during adenosine infusion. Left ventricular blood pool and myocardium were segmented on dynamic PET data by NMF method. Myocardial blood flow (MBF) was calculated from input and tissue functions by a single compartmental model with correction of partial volume and spillover effects. Results: There were no significant difference in resting MBF between the two groups (Smokers: 1.43 0.41 ml/g/min and non-smokers: $1.37{\pm}0.41$ ml/g/min p=NS). during cold pressor stimulation, MBF in smokers was significantly lower than 4hat in non-smokers ($1.25{\pm}0.34$ ml/g/min vs $1.59{\pm}0.29$ ml/gmin; p=0.019). The difference in the ratio of cold pressor MBF to resting MBF between the two groups was also significant (p=0.024; $90{\pm}24%$ in smokers and $122{\pm}28%$ in non-smokers.). During adenosine infusion, however, hyperemic MBF did not differ significantly between smokers and non-smokers ($5.81{\pm}1.99$ ml/g/min vs $5.11{\pm}1.31$ ml/g/min ; p=NS). Conclusion: in smokers, MBF during cold pressor stimulation was significantly lower compared wi4h nonsmokers, reflecting smoking-Induced endothelial dysfunction. However, there was no significant difference in MBF during adenosine-induced hyperemia between the two groups.

용용과 모델 구성을 중시하는 수학과 교육 과정 개발 방안 탐색

  • Jeong Eun Sil
    • The Mathematical Education
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    • v.30 no.1
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    • pp.1-19
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    • 1991
  • This study intends to provide some desirable suggestions for the development of application oriented mathematics curriculum. More specific objects of this study is: 1. To identify the meaning of application and modelling in mathematics curriculm. 2. To illuminate the historical background of and trends in application and modelling in the mathematics curricula. 3. To consider the reasons for including application and modelling in the mathematics curriculum. 4. To find out some implication for developing application oriented mathematics curriculum. The meaning of application and modelling is clarified as follows: If an arbitrary area of extra-mathematical reality is submitted to any kind of treatment which invovles mathematical concepts, methods, results, topics, we shall speak of the process of applying mathemtaics to that area. For the result of the process we shall use the term an application of mathematics. Certain objects, relations between them, and structures belonging to the area under consideration are selected and translated into mathemtaical objects, relation and structures, which are said to represent the original ones. Now, the concept of mathematical model is defined as the collection of mathematical objcets, . relations, structures, and so on, irrespective of what area is being represented by the model and how. And the full process of constructing a mathematical model of a given area is called as modelling, or model-building. During the last few decades an enormous extension of the use of mathemtaics in other disciplines has occurred. Nowadays the concept of a mathematical model is often used and interest has turned to the dynamic interaction between the real world and mathematics, to the process translating a real situation into a mathematical model and vice versa. The continued growing importance of mathematics in everyday practice has not been reflected to the same extent in the teaching and learning of mathematics in school. In particular the world-wide 'New Maths Movement' of the 19608 actually caused a reduction of the importance of application and modelling in mathematics teaching. Eventually, in the 1970s, there was a reaction to the excessive formallism of 'New Maths', and a return in many countries to the importance of application and connections to the reality in mathematics teaching. However, the main emphasis was put on mathematical models. Applicaton and modelling should be part of the mathematics curriculum in order to: 1. Convince students, who lacks visible relevance to their present and future lives, that mathematical activities are worthwhile, and motivate their studies. 2. Assist the acqusition and understanding of mathematical ideas, concepts, methods, theories and provide illustrations and interpretations of them. 3. Prepare students for being able to practice application and modelling as private individuals or as citizens, at present or in the future. 4. Foster in students the ability to utilise mathematics in complex situations. Of these four reasons the first is rather defensive, serving to protect or strengthen the position of mathematics, whereas the last three imply a positive interest in application and modelling for their own sake or for their capacity to improve mathematics teaching. Suggestions, recomendations and implications for developing application oriented mathematics curriculum were made as follows: 1. Many applications and modelling case studies suitable for various levels should be investigated and published for the teacher. 2. Mathematics education both for general and vocational students should encompass application and modelling activities, of a constructive as well as analytical and critical nature. 3. Application and modelling activities should. be introduced in mathematics curriculum through the interdisciplinary integrated approach. 4. What are the central ideas of, and what are less-important topics of application-oriented curriculum should be studied and selected. 5. For any mathematics teacher, application and modelling should form part of pre- and in-service education.

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