• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.405-413
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• 2004

Rational parameterization of curves and surfaces is one of the main topics in computer-aided geometric design because of their computational advantages. Pythagorean hodograph (PH) curves and Minkowski Pythagorean hodograph (MPH) curves have attracted many researcher's interest because they provide for rational representation of their offset curves in Euclidean space and Minkowski space, respectively. In [10], Kim presented the characterization of the PH curves in the Euclidean space and analyzed the relation between the class of PH curves and the class of rational curves. In this paper, we extend the characterization of PH curves in [10] into that of MPH curves in the general Minkowski space and consider some generalized MPH curves satisfying this characterization.

• Genomics & Informatics
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• v.9 no.3
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• pp.127-133
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• 2011

The Epstein-Barr virus-transformed lymphoblastoid cell line (LCL) is one of the major genomic resources for human genetics and immunological studies. Use of LCLs is currently extended to pharmacogenetic studies to investigate variations in human gene expression as well as drug responses between individuals. We evaluated four common internal controls for gene expression analysis of selected hematopoietic transcriptional regulatory genes between B cells and LCLs. In this study, the expression pattern analyses showed that TBP (TATA box-binding protein) is a suitable internal control for normalization, whereas GAPDH (glyceraldehyde-3-phosphate dehydrogenase) is not a good internal control for gene expression analyses of hematopoiesis-related genes between B cells and LCLs at different subculture passages. Using the TBP normalizer, we found significant gene expression changes in selected hematopoietic transcriptional regulatory genes (downregulation of RUNX1, RUNX3, CBFB, TLE1, and NOTCH2 ; upregulation of MSC and PLAGL2) between B cells and LCLs at different passage numbers. These results suggest that these hematopoietic transcriptional regulatory genes are potential cellular targets of EBV infection, contributing to EBV-mediated B-cell transformation and LCL immortalization.