• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.523-537
• /
• 2011

A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the $L_1$ distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.

• Structural Engineering and Mechanics
• /
• v.62 no.3
• /
• pp.303-310
• /
• 2017

The model updating problems, which are to find the optimal approximation to the discrete quadratic model obtained by the finite element method, are critically important to the vibration analysis. In this paper, the structured model updating problem is considered, where the coefficient matrices are required to be symmetric and positive semidefinite, represent the interconnectivity of elements in the physical configuration and minimize the dynamics equations, and furthermore, due to the physical feasibility, the physical parameters should be positive. To the best of our knowledge, the model updating problem involving all these constraints has not been proposed in the existed literature. In this paper, based on the semidefinite programming technique, we design a general-purpose numerical algorithm for solving the structured model updating problems with incomplete measured data and present some numerical results to demonstrate the effectiveness of our method.

• The Mathematical Education
• /
• v.53 no.3
• /
• pp.413-434
• /
• 2014

Logic lays the foundation of Mathematics and the development of Mathematics is dependent on critical thinking. So it is important that school mathematics helps students develop their logical and critical thinking ability for both mathematics learning and problem solving in general. MINDSTORMS, a LEGO based programming activity kit, is an effective teaching and learning tool that can be used to enhance logical and critical thinking in students. This study focused on measuring the growth of students' ability to think logically and critically when they used MINDSTORMS activities to learn programming. In addition, we investigated how the students' logical and critical thinking changed from the MINDSTORMS learning experience. The study confirmed that the programming activities using MINDSTORMS help to enhance logical and critical thinking in students. The students attitude about logical and critical thinking became more positive and the activities helped to engage students to think logically and critically. This type of programming activities should be valuable in mathematics education and it should be included in a general mathematics curriculum.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.75-106
• /
• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• Journal of Fisheries and Marine Sciences Education
• /
• v.25 no.5
• /
• pp.1020-1030
• /
• 2013

The purpose of this study was to develop the STEAM educational program based on the computer programming. STEAM education has been recently attracted to a lot of people. We had a focus of computer science in STEM fields. We used the programming language f or learning KODU. We selected appropriate topics for STEAM education and learning programming. We developed the educational program of 30 hours about selected topics and had classes for 4th and 5th grade elementary students. In order to verify the effectiveness of the educational program, we analyzed the results of pre- and posttest about GALT(Group Assessment of Logical Thinking), TTCT(Torrance Tests of Creative Thinking), science-related affective domain, and mathematical interests and attitudes tests. In the analysis results, the education program we developed had positive impacts on creativity, logical thinking, and science-related affective domain of elementary school students.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.753-765
• /
• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.

• Journal of Korean Society of Rural Planning
• /
• v.26 no.3
• /
• pp.25-38
• /
• 2020

The purpose of this study is constructing a regional-level crop acreage choice model incorporating the impacts of producer risk aversion, and applying the constructed model to the Korean policy that promotes rice paddy conversion into non-rice crop fields. The study adopts the approach of Paris (2018) which estimates the absolute risk aversion coefficient inside of a positive mathematical programming model. A panel data set of 143 cities/counties is used for the empirical study where agricultural land in each region is allocated to 8 crops. Our estimated absolute risk aversion coefficients are smaller than those of Paris (2018), but are a little bit larger than those of the existing Korea studies based on survey or econometric methods. We found that there are close relationships among the estimated risk aversion, regional characteristics, and farming patterns. We also found that incorporating the estimated risk attitudes results in substantial differences in the impacts of the rice paddy conversion policy.

• Journal of The Korean Association of Information Education
• /
• v.14 no.3
• /
• pp.319-328
• /
• 2010

Computer programming education gives students a chance to use computers independently and actively. This plays a very positive role in acquiring higher cognitive skills such as mathematical skills and creative logical thinking. Thus the purpose of this study is to measure the degrees of students' problem-solving abilities using MCU programming kits based on the ICT Education Guide. The experiment confirms that programming classes using MCU kits have a more positive effect on the students problem-solving abilities than do those using the existing computer textbooks. The sub-constituents of problem-solving abilities - problem recognition, information gathering, analysis, diffuse thinking, decision-making, planning, execution, evaluation and feedback - also show significant statistical differences. Therefore, we can conclude that programming classes using MCU kits are very effective in advancing problem-solving abilities.

• International Journal of Computer Science & Network Security
• /
• v.22 no.1
• /
• pp.105-112
• /
• 2022

The development and spread of IT-technologies has raised interest in teaching programming pupils. The article deals with problems related to programming and ways to overcome them. The importance of programming skills is emphasized, as this process promotes the formation of algorithmic thinking of pupils. The authors determined the level of pupils' interest to programing learning depending on the age. The analysis has showed that the natural interest of younger pupils in programming is decreasing over the years and in the most productive period of its study is minimized. It is revealed that senior school pupils are characterized by low level of interest in the study of programming; lack of motivation; the presence of psychological blocks on their own abilities in the context of programming; law level of computer science understanding. To overcome these problems, we conducted the second stage of the experiment, which was based on a change in the approach to programing learning, which involved pupils of non-specialized classes of senior school (experimental group). During the study of programming, special attention was paid to the motivational and psychological component, as well as the use of game technologies and teamwork of pupils. The results of the pedagogical experiment on studying the effectiveness of teaching programming for pupils of nonspecialized classes are presented. Improvement of the results provided the use of social and cognitive motives; application of verbal and non-verbal, external and internal means; communicative attacks; stimulation and psychological setting; game techniques, independent work and reflection, teamwork. The positive effect of the implemented methods is shown by the results verified by the methods of mathematical statistics in the experimental and control groups of pupils.

• East Asian mathematical journal
• /
• v.36 no.2
• /
• pp.317-330
• /
• 2020

The purpose of this action research project was to study the effects of incorporating coding into the middle school math classroom affected student dispositions with math and their understanding of mathematical concepts. The project, involving a total of 107 US middle school students, used five data sources to examine these effects: a survey, a chart measuring student engagement, a pre- and post-assessment before and after the coding project, and teacher observation with reflection forms. After analyzing the data, it was found that incorporating coding into the middle school math classroom could have a positive impact on student math dispositions and their understanding of math concepts.