• 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.

• Journal of Intelligence and Information Systems
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• v.21 no.3
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• pp.79-99
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• 2015

The prediction of bankruptcy has been extensively studied in the accounting and finance field. It can have an important impact on lending decisions and the profitability of financial institutions in terms of risk management. Many researchers have focused on constructing a more robust bankruptcy prediction model. Early studies primarily used statistical techniques such as multiple discriminant analysis (MDA) and logit analysis for bankruptcy prediction. However, many studies have demonstrated that artificial intelligence (AI) approaches, such as artificial neural networks (ANN), decision trees, case-based reasoning (CBR), and support vector machine (SVM), have been outperforming statistical techniques since 1990s for business classification problems because statistical methods have some rigid assumptions in their application. In previous studies on corporate bankruptcy, many researchers have focused on developing a bankruptcy prediction model using financial ratios. However, there are few studies that suggest the specific types of bankruptcy. Previous bankruptcy prediction models have generally been interested in predicting whether or not firms will become bankrupt. Most of the studies on bankruptcy types have focused on reviewing the previous literature or performing a case study. Thus, this study develops a model using data mining techniques for predicting the specific types of bankruptcy as well as the occurrence of bankruptcy in Korean small- and medium-sized construction firms in terms of profitability, stability, and activity index. Thus, firms will be able to prevent it from occurring in advance. We propose a hybrid approach using two artificial neural networks (ANNs) for the prediction of bankruptcy types. The first is a back-propagation neural network (BPN) model using supervised learning for bankruptcy prediction and the second is a self-organizing map (SOM) model using unsupervised learning to classify bankruptcy data into several types. Based on the constructed model, we predict the bankruptcy of companies by applying the BPN model to a validation set that was not utilized in the development of the model. This allows for identifying the specific types of bankruptcy by using bankruptcy data predicted by the BPN model. We calculated the average of selected input variables through statistical test for each cluster to interpret characteristics of the derived clusters in the SOM model. Each cluster represents bankruptcy type classified through data of bankruptcy firms, and input variables indicate financial ratios in interpreting the meaning of each cluster. The experimental result shows that each of five bankruptcy types has different characteristics according to financial ratios. Type 1 (severe bankruptcy) has inferior financial statements except for EBITDA (earnings before interest, taxes, depreciation, and amortization) to sales based on the clustering results. Type 2 (lack of stability) has a low quick ratio, low stockholder's equity to total assets, and high total borrowings to total assets. Type 3 (lack of activity) has a slightly low total asset turnover and fixed asset turnover. Type 4 (lack of profitability) has low retained earnings to total assets and EBITDA to sales which represent the indices of profitability. Type 5 (recoverable bankruptcy) includes firms that have a relatively good financial condition as compared to other bankruptcy types even though they are bankrupt. Based on the findings, researchers and practitioners engaged in the credit evaluation field can obtain more useful information about the types of corporate bankruptcy. In this paper, we utilized the financial ratios of firms to classify bankruptcy types. It is important to select the input variables that correctly predict bankruptcy and meaningfully classify the type of bankruptcy. In a further study, we will include non-financial factors such as size, industry, and age of the firms. Thus, we can obtain realistic clustering results for bankruptcy types by combining qualitative factors and reflecting the domain knowledge of experts.

• The Korean Journal of Food And Nutrition
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• v.15 no.2
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• pp.112-118
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• 2002

Sporulation in the fission yeast Schizosaccharomyces pombe has been regarded as an important model of cellular development and differentiation. S. pombe cells proliferate by mitosis and binary fission on growth medium. Deprivation of nutrients especially nitrogen sources, causes the cessation of mitosis and initiates sexual reproduction by matting between two sexually compatible cell types. Meiosis is then followed in a diploid cell in the absence of nitrogen source. DNA fragment complemented with the mutations of sporulation gene was isolated from the S. pombe gene library constructed in the vector, pDB 248' and designated as pDB(spo5)1. We futher analyzed six recombinant plasmids, pDB(spo5)2, pDB(spo5)3, pDB(spo5)4, pDB(spo5)5, pDB (spo5)6, pDB(spo5)7 and found each of these plasmids is able to rescue the spo5-2, spo5-3, spo5-4, spo5-5, spo5-6, spo5-7 mutations, respectively. Mapping of the integrated plasmid into the homologous site of the S. pombe chromosomes demonstrated that pDB(spo5)1, and pDB(spu5)Rl contained the spo5 gene. Transcripts of spo5 gene were analyzed by Northern hybridization. Two transcripts of 3.2 kb and 2.5kb were detected with 5kb Hind Ⅲ fragment containing a part of the spo5 gene as a probe. The small mRNA(2.5kb) appeared only when a wild-type strain was cultured in the absence of nitrogen source in which condition the large mRNA (3.2kb) was produced constitutively. Appearance of a 2.5kb spo5-mRNA depends upon the function of the meil, mei2 and mei3 genes.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.12a
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• pp.169-181
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• 2004

SK Telecom has already constructed GIMS system as the base common framework of LBS/GIS service system based on OGC(OpenGIS Consortium)'s international standard for the first mobile vector map service in 2002, But as service content appears more complex, renovation has been needed to satisfy multi-purpose, multi-function and maximum efficiency as requirements have been increased. This research is for preparation ion of GML3-based platform to upgrade service from GML2 based GIMS system. And with this, it will be possible for variety of application services to provide location and geographic data easily and freely. In GML 3.0, it has been selected animation, event handling, resource for style mapping, topology specification for 3D and telematics services for mobile LBS multimedia service. And the schema and transfer protocol has been developed and organized to optimize data transfer to MS(Mobile Stat ion) Upgrade to GML 3.0-based GIMS system has provided innovative framework in the view of not only construction but also service which has been implemented and applied to previous research and system. Also GIMS channel interface has been implemented to simplify access to GIMS system, and service component of GIMS internals, WFS and WMS, has gotten enhanded and expanded function.