• ETRI Journal
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• 제36권1호
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• pp.167-170
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• 2014

In this letter, we propose an unsupervised framework for speech noise reduction based on the recent development of low-rank and sparse matrix decomposition. The proposed framework directly separates the speech signal from noisy speech by decomposing the noisy speech spectrogram into three submatrices: the noise structure matrix, the clean speech structure matrix, and the residual noise matrix. Evaluations on the Noisex-92 dataset show that the proposed method achieves a signal-to-distortion ratio approximately 2.48 dB and 3.23 dB higher than that of the robust principal component analysis method and the non-negative matrix factorization method, respectively, when the input SNR is -5 dB.

• 호남수학학술지
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• 제28권3호
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• pp.333-342
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• 2006

We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A is an SN-matrix provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of A is S, for each A ${\in}$ Q(A). We have a characterization of an SN-matrix related with L-matrix and we analyze the structure of an SN-matrix.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권11호
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• pp.5616-5630
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• 2019

Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.'s work. We improve Mishra et al.'s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.'s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.'s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.

• 대한수학회지
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• 제50권4호
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• 한국진공학회지
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• 제1권1호
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• pp.115-120
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• 1992

SIMS는 뛰어난 원소검출감도와 깊이 분해능을 가지고 있어서 깊이에 따른 미량불 순물 분석에 필수적인 장비이지만, 시료와 불순물의 변화에 따라 이온화율과 깍이는 속도가 달라서 일어나는 matrix effect 때문에 표준 시료없이 정량분석을 할 수 없는 문제점이 있 다. 이런 SIMS의 단점을 보완하기 위한 방법으로 개발된 여러 가지 SNMS 기술 중 SIMS에 아무런 기계장치를 덧붙이지 않고도 정량화 개선효과를 가져오는 CsX+ SNMS에 대한 연구 를 진행하여, 지금까지 밝혀진 실리콘 산화막 등에서의 주성분원소 조성비분석을 통해 SNMS 기능을 확인하고 SIMS의 주 분석대상인 분순물 농도분석에의 적용가능성을 실험해 보았다. 이를 위해 실리콘에 BF2 이온 주입 후 붕소분포 분석시 강한 matrix effect를 나타 내는 불소의 효과를 SNMS와 SIMS로 비교하였으며, 검출한계와 dynamic range도 조사하였 다. 실험결과 CsX+ SNMS 기술은 matrix effect 때문에 실제분포와 다른 값으로 검출되는 불순물 시료분석에 적용할 수 있음을 알았다.

• 대한수학회논문집
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• 제12권2호
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• pp.269-273
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• 1997

We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular stochastic totally positive matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ Jacobi intensity matrices.

• Bioinformatics and Biosystems
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• 제2권1호
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• pp.7-11
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• 2007

하나의 아미노산이 다른 아미노산으로 바뀌는 가능성을 계통학적인 나무를 이용해서 치환행렬로 만들었다. PFMT(Phylogenetic Focused Mutaion Tendency)행렬은 기존의 PAM160이나 BLOSUM62와 다르게 공통조상으로부터 상위 종으로 치환되는 가능성을 점수화 하였다. COGs의 데이터베이스에 있는 152KOGs를 뽑아서 아미노산의 치환횟수를 점수화하였다. PFMT 행렬은 어떤 서열보다 더 상위 종의 서열을 비교할 때 유용하게 쓰일 수 있으며 2개의 아미노산간의 치환 관계를 더 자세하게 볼 수 있게 한다.