• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.113-123
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• 2006

Normal mixture model(NMM) frequently used to cluster genes on microarray gene expression data. In this paper some of component means of NMM are modelled by a linear regression model so that its design matrix presents the pattern between sample classes in microarray matrix. This modelling for the component means by given design matrices certainly has an advantage that we can lead the clusters that are previously designed. However, it suffers from 'overfitting' problem because in practice genes often are highly dimensional. This problem also arises when the NMM restricted by the linear model for component-means is fitted. To cope with this problem, in this paper, the use of the factor analyzer NMM restricted by linear model is proposed to cluster genes. Also several design matrices which are useful for clustering genes are provided.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.305-320
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• 2020

This study aims to generalize MINRES-N2 method [1]. It means that we tend to obtain an algorithm to transfer each normal matrix - that its eigenvalues belong to an algebraic curve of low degree k- to its condensed form through using a unitary similarity transformation. Then, we aim to obtain a method to solve a system of linear equations that its coefficient matrix is equal to such a matrix by utilizing it. Finally this method is compared to the well-known GMRES method through using numerical examples. The results obtained through examples show that the given method is more efficient than GMRES.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.673-683
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• 2009

We point out: to make Hermtian matrices A and B satisfy Styan matrix inequality, the condition "positive definite property" demanded in the present literatures is not necessary. Furthermore, on the premise of abandoning positive definite property, we derive Styan matrix inequality of Hadamard product for inverse Hermitian matrices and the sufficient and necessary conditions that the equation holds in our paper.

• Journal of information and communication convergence engineering
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• v.20 no.1
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• pp.58-64
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• 2022

Breast ultrasonic reading is critical as a primary screening test for the early diagnosis of breast cancer. However, breast ultrasound examinations show significant differences in diagnosis based on the difference in image quality according to the ultrasonic equipment, experience, and proficiency of the examiner. Accordingly, studies are being actively conducted to analyze the texture characteristics of normal breast tissue, positive tumors, and malignant tumors using breast ultrasonography and to use them for computer-assisted diagnosis. In this study, breast ultrasonography was conducted to select 247 ultrasound images of 71 normal breast tissues, 87 fibroadenomas among benign tumors, and 89 malignant tumors. The selected images were calculated using a statistical method with 21 feature parameters extracted using the gray level co-occurrence matrix algorithm, and classified as normal breast tissue, benign tumor, and malignancy. In addition, we proposed five feature parameters that are available for computer-aided diagnosis of breast cancer classification. The average classification rate for normal breast tissue, benign tumors, and malignant tumors, using this feature parameter, was 82.8%.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.53-60
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• 1999

We find bounds of eigenvalues of bipartite tournament matrices. We see when bipartite matrices exist and how players and teams of the matrices are evenly ranked. Also, we show that a bipartite tournament matrix can be both regular and normal when and only when it has the same team size.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.49-56
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• 2004

Model updating is a very active research field, in which significant efforts has been invested in recent years. Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are-unavoidably-corrupted with uncorrected noise content. In this paper, Reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. One simulated system is employed to illustrate the applicability of the proposed method. The result indicate that the damping matrix of correlated finite element model can be identified accurately by the proposed method. In addition, the robustness of the new approach uniformly distributed measurement noise Is also addressed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.863-869
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• 2007

An improved method based on a normal frequency response function (FRF) is proposed to identify structural parameters such as mass, stiffness and damping matrices directly from the FRFs of a linear mechanical system. The method for estimating structural parameters directly from the measured FRFs of a structure is presented. This paper demonstrates that the characteristic matrices are extracted more accurately by using a weighted equation and eliminating the matrix inverse operation. The method is verified for a four degree-of-freedom lumped parameter system and an eight degree-of-freedom finite element beam. Experimental verification is also performed for a free-free steel beam whose size and physical properties are the same as those of the finite element beam. The results show that the structural parameters, especially the damping matrix, can be estimated more accurately by the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.813-822
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• 2014

A ring R is called quasipolar if for every a 2 R there exists $p^2=p{\in}R$ such that $p{\in}comm^2{_R}(a)$, $ a+p{\in}U(R)$ and $ap{\in}R^{qnil}$. The class of quasipolar rings lies properly between the class of strongly ${\pi}$-regular rings and the class of strongly clean rings. In this paper, we determine when a $2{\times}2$ matrix over a local ring is quasipolar. Necessary and sufficient conditions for a $2{\times}2$ matrix ring to be quasipolar are obtained.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.11a
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• pp.421-424
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• 2004

Model updating is a very active research field, in which significant efforts has been invested in recent years. Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are-unavoidably-corrupted with uncorrelated noise content. In this paper, Reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. Full scale pseudo dynamic pier test is employed to illustrate the applicability of the proposed method. The result indicate that the damping matrix of correlated finite element model can be identified accurately by the proposed method. In addition, the robustness of the new approach uniformly distributed measurement noise is also addressed.

• Journal of Korean Neurosurgical Society
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• v.40 no.5
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• pp.363-368
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• 2006

Objective : Little is known about the comprehensive molecular and biological mechanism on the development of the degeneration of the intervertebral disc. Many kinds of matrix metalloproteinase[MMP] initiate the degradation of the extracellular matrix including several kinds of collagens and proteoglycans. We compared molecular and immunohistochemical features of degenerated intervertebral disc and normal counterparts in order to investigate the role of MMP-1, 2, 3, 9. Methods : We have evaluated MMP-1, 2, 3, 9 expression in 30 surgically resected lumbar disc from degenerative disc disease patients and 5 normal control cases. RT-PCR[reverse transcriptase-polymerase chain reaction] and immunohistochemistry were performed. Results : By RT-PCR, normal tissue samples showed merely scant expression of MMP-1, 2, 3, 9 mRNA, but degenerated disc samples revealed more pronounced expression. mRNA amplifications were detected in 60%, 63.3%, 70%, 53.3% cases By immunohistochemistry, normal tissue samples showed minimal protein expression of MMP-1, 2, 3, 9, but degenerated disc samples revealed more pronounced expression. Protein expressions were detected in 73.3%, 63.3%, 76.7%, 63.3% cases. Both the mRNA amplification and protein overexpression rates were significantly higher in degenerated disc than in the normal tissue. Concordance between both the mRNA amplification and protein expressions of MMP-1, 3, 9 were not observed, but there is well correlation in MMP-2 expression. Conclusion : We concluded that the over-expressions of the MMP-1, 2, 3, 9 may contribute to the development of degeneration of the intervertebral disc.