• Title, Summary, Keyword: factor rank

### FACTOR RANK COMPARISONS OF MATRICES OVER TWO RELATED SEMIRINGS

• Song Seok-Zun
• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.219-226
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• 2006
• We consider matrices whose entries can be viewed as elements of both nonnegative integers and nonnegative rational numbers. We determine the differences of factor rank of matrices over the two semirings.

### RANK PRESERVER OF BOOLEAN MATRICES

• SONG, SEOK-ZUN;KANG, KYUNG-TAE;JUN, YOUNG-BAE
• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.501-507
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• 2005
• A Boolean matrix with rank 1 is factored as a left factor and a right factor. The perimeter of a rank-1 Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

### Factor Rank and Its Preservers of Integer Matrices

• Song, Seok-Zun;Kang, Kyung-Tae
• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.581-589
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• 2006
• We characterize the linear operators which preserve the factor rank of integer matrices. That is, if $\mathcal{M}$ is the set of all $m{\times}n$ matrices with entries in the integers and min($m,n$) > 1, then a linear operator T on $\mathcal{M}$ preserves the factor rank of all matrices in $\mathcal{M}$ if and only if T has the form either T(X) = UXV for all $X{\in}\mathcal{M}$, or $m=n$ and T(X)=$UX^tV$ for all $X{\in}\mathcal{M}$, where U and V are suitable nonsingular integer matrices. Other characterizations of factor rank-preservers of integer matrices are also given.

### RANK INEQUALITIES OVER SEMIRINGS

• BEASLEY LeRoy B.;GUTERMAN ALEXANDER E.
• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.223-241
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• 2005
• Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.

### RANK Signaling Pathways and Key Molecules Inducing Osteoclast Differentiation

• Lee, Na Kyung
• Biomedical Science Letters
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• v.23 no.4
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• pp.295-302
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• 2017
• Mononuclear osteoclast precursors derived from hematopoietic progenitors fuse together and then become multinucleated mature osteoclasts by macrophage-colony stimulating factor (M-CSF) and receptor activator of nuclear factor-${\kappa}B$ ligand (RANKL). Especially, the binding of RANKL to its receptor RANK provides key signals for osteoclast differentiation and bone-resorbing function. RANK transduces intracellular signals by recruiting adaptor molecules such as TNFR-associated factors (TRAFs), which then activate mitogen activated protein kinases (MAPKs), Src/PI3K/Akt pathway, nuclear factor-${\kappa}B$ (NF-${\kappa}B$) and finally amplify NFATc1 activation for the transcription and activation of osteoclast marker genes. This review will briefly describe RANKL-RANK signaling pathways and key molecules critical for osteoclast differentiation.

### TAK1-dependent Activation of AP-1 and c-Jun N-terminal Kinase by Receptor Activator of NF-κB

• Lee, Soo-Woong;Han, Sang-In;Kim, Hong-Hee;Lee, Zang-Hee
• BMB Reports
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• v.35 no.4
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• pp.371-376
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• 2002
• The receptor activator of nuclear factor kappa B (RANK) is a member of the tumor necrosis factor (TNF) receptor superfamily. It plays a critical role in osteoclast differentiaion, lymph node organogenesis, and mammary gland development. The stimulation of RANK causes the activation of transcription factors NF-${\kappa}B$ and activator protein 1 (AP1), and the mitogen activated protein kinase (MAPK) c-Jun N-terminal kinase (JNK). In the signal transduction of RANK, the recruitment of the adaptor molecules, TNF receptor-associated factors (TRAFs), is and initial cytoplasmic event. Recently, the association of the MAPK kinase kinase, transforming growth factor-$\beta$-activated kinase 1 (TAK1), with TRAF6 was shown to mediate the IL-1 signaling to NF-${\kappa}B$ and JNK. We investigated whether or not TAK1 plays a role in RANK signaling. A dominant-negative form of TAK1 was discovered to abolish the RANK-induced activation of AP1 and JNK. The AP1 activation by TRAF2, TRAF5, and TRAF6 was also greatly suppressed by the dominant-negative TAK1. the inhibitory effect of the TAK1 mutant on RANK-and TRAF-induced NF-${\kappa}B$ activation was also observed, but less efficiently. Our findings indicate that TAK1 is involved in the MAPK cascade and NF-${\kappa}B$ pathway that is activated by RANK.

### Current Understanding of RANK Signaling in Osteoclast Differentiation and Maturation

• Park, Jin Hee;Lee, Na Kyung;Lee, Soo Young
• Molecules and Cells
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• v.40 no.10
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• pp.706-713
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• 2017
• Osteoclasts are bone-resorbing cells that are derived from hematopoietic precursor cells and require macrophage-colony stimulating factor and receptor activator of nuclear factor-${\kappa}B$ ligand (RANKL) for their survival, proliferation, differentiation, and activation. The binding of RANKL to its receptor RANK triggers osteoclast precursors to differentiate into osteoclasts. This process depends on RANKL-RANK signaling, which is temporally regulated by various adaptor proteins and kinases. Here we summarize the current understanding of the mechanisms that regulate RANK signaling during osteoclastogenesis. In the early stage, RANK signaling is mediated by recruiting adaptor molecules such as tumor necrosis factor receptorassociated factor 6 (TRAF6), which leads to the activation of mitogen-activated protein kinases (MAPKs), and the transcription factors nuclear factor-${\kappa}B$ (NF-${\kappa}B$) and activator protein-1 (AP-1). Activated NF-${\kappa}B$ induces the nuclear factor of activated T-cells cytoplasmic 1 (NFATc1), which is the key osteoclastogenesis regulator. In the intermediate stage of signaling, the co-stimulatory signal induces $Ca^{2+}$ oscillation via activated phospholipase $C{\gamma}2$ ($PLC{\gamma}2$) together with c-Fos/AP-1, wherein $Ca^{2+}$ signaling facilitates the robust production of NFATc1. In the late stage of osteoclastogenesis, NFATc1 translocates into the nucleus where it induces numerous osteoclast-specific target genes that are responsible for cell fusion and function.

### Development of Research Personnel Evaluation System Using Median Rank (Median Rank를 이용한 연구인력 평가 시스템)

• 이성기;윤덕균
• Journal of the Society of Korea Industrial and Systems Engineering
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• v.21 no.47
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• pp.169-179
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• 1998
• Median rank is used to systemize the evaluation of research personnel in a research institution. Suggested evaluation system is purposed to enhance the fairness, distinguish the factors of evaluation and maximize the synergy of researchers. The factors of evaluation are largely divided into the subjective and the objective factor. The final rank of the researchers is determined with the converted median rank value. The propriety of applying median rank is tested by Spearman's rank correlation coefficient. We also suggest the method of determining the rank of researchers. This evaluation system is not fixed in special case but can be changed in situation. It also can be applied to any other personnel evaluation system through the appropriate revision.

### Nonparametric test for cointegration rank using Cholesky factor bootstrap

• Lee, Jin
• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.587-592
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• 2016
• It is a long-standing issue to correctly determine the number of long-run relationships among time series processes. We revisit nonparametric test for cointegration rank and propose bootstrap refinements. Consistent with model-free nature of the tests, we make use of Cholesky factor bootstrap methods, which require weak conditions for data generating processes. Simulation studies show that the original Breitung's test have difficulty in obtaining the correct size due to dependence in cointegrated errors. Our proposed bootstrapped tests considerably mitigate size distortions and represent a complementary approach to other bootstrap refinements, including sieve methods.

### Tests of Factor Effect Using Saturated Design in $K^n$ Factorial Design ($K^n$ 요인배치법에서 포화실험에 의한 요인효과의 검정)

• Choi, Sung-Woon
• Proceedings of the Safety Management and Science Conference
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• pp.295-299
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• 2008
• This paper discusses tests of factor effect or contrast by the use of saturated design $k^n$ factorial design. The nine nonparametric rank measures in normality test using normal probability pot are proposed. Length's PSE(Pseduo Standard Error) test [4] which relies on the concept of effect sparsity is also introduced and extended to the margin of error(ME) and Simultaneous margin of error(SME).