• East Asian mathematical journal
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• v.40 no.2
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• pp.209-229
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• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• School Mathematics
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• v.10 no.1
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• pp.23-42
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• 2008

The purpose of this study was to describe characteristics of thinking in elementary gifted students' solutions to algebraic tasks. Especially, this paper was focused on the students' strategies to develop generalization while problem solving, the justifications on the generalization and metacognitive thinking emerged in stildents' problem solving process. To find these issues, a case study was conducted. The subjects of this study were four 6th graders in elementary school-they were all receiving education for the gifted in an academy for the gifted attached to a university. Major findings of this study are as follows: First, during the process of the task solving, the students varied in their use of generalization strategies and utilized more than one generalization strategy, and the students also moved from one strategy toward other strategies, trying to reach generalization. In addition, there are some differences of appling the same type of strategy between students. In a case of reaching a generalization, students were asked to justify their generalization. Students' justification types were different in level. However, there were some potential abilities that lead to higher level although students' justification level was in empirical step. Second, the students utilized their various knowledges to solve the challengeable and difficult tasks. Some knowledges helped students, on the contrary some knowledges made students struggled. Specially, metacognitive knowledges of task were noticeably. Metacognitive skills; 'monitoring', 'evaluating', 'control' were emerged at any time. These metacognitive skills played a key role in their task solving process, led to students justify their generalization, made students keep their task solving process by changing and adjusting their strategies.

• Journal of KIISE:Software and Applications
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• v.30 no.3_4
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• pp.326-338
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• 2003

The objective of a neural network design and model selection is to construct an optimal network with a good generalization performance. However, training data include noises, and the number of training data is not sufficient, which results in the difference between the true probability distribution and the empirical one. The difference makes the teaming parameters to over-fit only to training data and to deviate from the true distribution of data, which is called the overfitting phenomenon. The overfilled neural network shows good approximations for the training data, but gives bad predictions to untrained new data. As the complexity of the neural network increases, this overfitting phenomenon also becomes more severe. In this paper, by taking statistical viewpoint, we proposed an integrative process for neural network design and model selection method in order to improve generalization performance. At first, by using the natural gradient learning with adaptive regularization, we try to obtain optimal parameters that are not overfilled to training data with fast convergence. By adopting the natural pruning to the obtained optimal parameters, we generate several candidates of network model with different sizes. Finally, we select an optimal model among candidate models based on the Bayesian Information Criteria. Through the computer simulation on benchmark problems, we confirm the generalization and structure optimization performance of the proposed integrative process of teaming and model selection.

• Language and Information
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• v.4 no.2
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• pp.41-54
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• 2000

In this paper we present a unified account for -ina a Korean particle which displays a few unexpected differences from English, or despite the fact that they are in a virtual counterpart relation in coordination between the two languages We first reach an empirical generalization that -ina use mostly in a disjunctive coordination is construed conjunctively in a generic sentence. Then we conclude that the various use of -ina can be naturally accounted for by modifying the notion of 'second-best set' in the existing work of K Lee(1993).(Kyung Hee University)

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.363-386
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• 2014

This paper has improved several ratio type estimators of the population median including their generalization in the presence of three known quartiles of an auxiliary variable. The properties of the improved estimators are discussed and applied. Both the empirical and simulation studies confirm that our new estimators perform efficiently.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1830-1835
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• 2003

A novel index representing burden distribution form in the blast furnace is developed and index estimation model is built with an empirical modeling method to monitor inner condition of the furnace without expensive sensors. To find the best combination of index and modeling method, two candidates for the index and four modeling methods have been examined. Results have shown that 3-D index have more resolution in describing the distribution form than 1-D index and ANN model produces smallest RMSE due to nonlinearity between the indices and charging mode. Although ANN has shown the best prediction accuracy in this study, PLS can be a good alternative due to its advantages in generalization capability, consistency, simplicity and training time. The second best result of PLS in the prediction results supports this fact.

• Computers and Concrete
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• v.17 no.4
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• pp.489-498
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• 2016

In this paper, the flexural strength ($f_{fs}$) and splitting tensile strength ($f_{sts}$) of concrete containing different proportions of fly ash have been modeled by using gene expression programming (GEP). Two GEP models called GEP-I and GEP-II are constituted to predict the $f_{fs}$ and $f_{sts}$ values, respectively. In these models, the age of specimen, cement, water, sand, aggregate, superplasticizer and fly ash are used as independent input parameters. GEP-I model is constructed by 292 experimental data and trisected into 170, 86 and 36 data for training, testing and validating sets, respectively. Similarly, GEP-II model is constructed by 278 experimental data and trisected into 142, 70 and 66 data for training, testing and validating sets, respectively. The experimental data used in the validating set of these models are independent from the training and testing sets. The results of the statistical parameters obtained from the models indicate that the proposed empirical models have good prediction and generalization capability.

• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.92-101
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• 1987

Our interest is to access in some way teh relative odds or probability that a multivariate observation Z belongs to one of k multivariate normal populations with unequal covariance matrices. We derived the empirical Bayes posterior odds ratio for the classification rule when population parameters are unknown. It is a generalization of the posterior odds ratio suggested by Gelsser (1964). The classification rule does not have complicated distribution theory which a large variety of techniques from the sampling viewpoint have. The proposed posterior odds ratio is compared to the Gelsser's posterior odds ratio through a Monte Carlo study. The results show that the empiricla Bayes posterior odds ratio, in general, performs better than the Gelsser's. Especially, for large dimension of Z and small training sample, the performance is prominent.

• International Journal of Computer Science & Network Security
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• v.23 no.9
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• pp.71-76
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• 2023

In order to achieve this goal, we consider the following issues: a retrospective analysis of the concepts of "giftedness", "intellectually gifted personality"; the experience of working with gifted youth abroad is analyzed; features of work with gifted student youth are revealed; educational and methodological support and practical work with gifted students are analyzed; an empirical study was conducted to determine the attitude of gifted youth to organizational forms of work with them; developed a scientific circle as a form of work with intellectually gifted student youth. A set of methods is used, in particular: theoretical methods: comparison, analysis, synthesis and generalization; empirical methods: analysis of documentation and results of pedagogical activity, observation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.4
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• pp.1441-1456
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• 2015

The bidimensional empirical mode decomposition (BEMD) algorithm with high adaptability is more suitable to process multiple image fusion than traditional image fusion. However, the advantages of this algorithm are limited by the end effects problem, multiscale integration problem and number difference of intrinsic mode functions in multiple images decomposition. This study proposes the multiscale self-coordination BEMD algorithm to solve this problem. This algorithm outside extending the feather information with the support vector machine which has a high degree of generalization, then it also overcomes the BEMD end effects problem with conventional mirror extension methods of data processing,. The coordination of the extreme value point of the source image helps solve the problem of multiscale information fusion. Results show that the proposed method is better than the wavelet and NSCT method in retaining the characteristics of the source image information and the details of the mutation information inherited from the source image and in significantly improving the signal-to-noise ratio.