The prognosis of hepatocellular carcinoma (HCC) still remains dismal, although many advances in its clinical study have been made. It is important for tumor control to identify the factors that predispose patients to ...The prognosis of hepatocellular carcinoma (HCC) still remains dismal, although many advances in its clinical study have been made. It is important for tumor control to identify the factors that predispose patients to death. With new discoveries in cancer biology, the pathological and biological prognostic factors of HCC have been studied quite extensively. Analyzing molecular markers (biomarkers) with prognostic significance is a complementary method. A large number of molecular factors have been shown to associate with the invasiveness of HCC, and have potential prognostic significance. One important aspect is the analysis of molecular markers for the cellular malignancy phenotype. These include alterations in DNA ploidy, cellular proliferation markers (PCNA, Ki-67, Mcm2, MIB1, MIA, and CSE1L/CAS protein), nuclear morphology, the p53 gene and its related molecule MD M2, other cell cycle regulators (cyclin A, cyclin D, cyclin E, cdc2, p27, p73), oncogenes and their receptors (such as ras, c-myc, c-fms, HGF, c-met, and erb-B receptor family members), apoptosis related factors (Fas and FasL), as well as telomerase activity. Another important aspect is the analysis of molecular markers involved in the process of cancer invasion and metastasis. Adhesion molecules (E-cadherin, catenins, serum intercellular adhesion molecule-1, CD44 variants), proteinases involved in the degradation of extracellular matrix (MMP-2, MMP-9, uPA, uPAR, PAI), as well as other molecules have been regarded as biomarkers for the malignant phenotype of HCC, and are related to prognosis and therapeutic outcomes. Tumor angiogenesis is critical to both the growth and metastasis of cancers including HCC, and has drawn much attention in recent years. Many angiogenesis-related markers, such as vascular endothelial growth factor (VEGF), basic fibroblast growth factor (bFGF), platelet-derived endothelial cell growth factor (PD-ECGF), thrombospondin (TSP), angiogenin, pleiotrophin, and endostatin (ES) levels, as well as intratumor microvessel density (M展开更多
INTRODUCTIONLiver fibrosis is a dynamic course leading tocirrhosis from a various chronic liver diseases. Thepathological basis of fibrosis is the disturbance ofproduction and degradation of the extracellularmatrix (E...INTRODUCTIONLiver fibrosis is a dynamic course leading tocirrhosis from a various chronic liver diseases. Thepathological basis of fibrosis is the disturbance ofproduction and degradation of the extracellularmatrix (ECM), which causes accumulation of ECMin the liver[1,2].展开更多
We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix...We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.展开更多
We know matrices and their transposes and we also know flip matrices. In my previous paper <i>Matrices-One Review</i>, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. ...We know matrices and their transposes and we also know flip matrices. In my previous paper <i>Matrices-One Review</i>, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would like to introduce water image of four matrices said above and properties of such matrices. Also we know, determinant of sum of matrices is not equal to sum of determinant of matrices. Why can’t we get equal value on addition side and additive side of determinant of matrix addition and subtraction? This question triggered me to find the reason. The basic algebra of mensuration gave ideas to retreat determinant of matrix addition and subtraction. I extent that ideas for matrices sum. Further, in 1812, French mathematician <b>Jacques Philippe Marie Binet</b> described how to multiply matrices. Matrices are defined on addition, subtraction and multiplication but not in division. By the inspiration of Binet, I would like to describe how to do divisions on matrices. This idea is derived from division of fractions. In division of fraction, reciprocal of divisor fraction multiplies with dividend fraction. I do the same in division on matrices with some modifications. By this way, we could find quotient matrix and remainder matrix which satisfy division algorithm. So we could say, determinant of division of dividend matrix and divisor matrix is equal to division of determinant of dividend matrix and determinant of divisor matrix.展开更多
文摘The prognosis of hepatocellular carcinoma (HCC) still remains dismal, although many advances in its clinical study have been made. It is important for tumor control to identify the factors that predispose patients to death. With new discoveries in cancer biology, the pathological and biological prognostic factors of HCC have been studied quite extensively. Analyzing molecular markers (biomarkers) with prognostic significance is a complementary method. A large number of molecular factors have been shown to associate with the invasiveness of HCC, and have potential prognostic significance. One important aspect is the analysis of molecular markers for the cellular malignancy phenotype. These include alterations in DNA ploidy, cellular proliferation markers (PCNA, Ki-67, Mcm2, MIB1, MIA, and CSE1L/CAS protein), nuclear morphology, the p53 gene and its related molecule MD M2, other cell cycle regulators (cyclin A, cyclin D, cyclin E, cdc2, p27, p73), oncogenes and their receptors (such as ras, c-myc, c-fms, HGF, c-met, and erb-B receptor family members), apoptosis related factors (Fas and FasL), as well as telomerase activity. Another important aspect is the analysis of molecular markers involved in the process of cancer invasion and metastasis. Adhesion molecules (E-cadherin, catenins, serum intercellular adhesion molecule-1, CD44 variants), proteinases involved in the degradation of extracellular matrix (MMP-2, MMP-9, uPA, uPAR, PAI), as well as other molecules have been regarded as biomarkers for the malignant phenotype of HCC, and are related to prognosis and therapeutic outcomes. Tumor angiogenesis is critical to both the growth and metastasis of cancers including HCC, and has drawn much attention in recent years. Many angiogenesis-related markers, such as vascular endothelial growth factor (VEGF), basic fibroblast growth factor (bFGF), platelet-derived endothelial cell growth factor (PD-ECGF), thrombospondin (TSP), angiogenin, pleiotrophin, and endostatin (ES) levels, as well as intratumor microvessel density (M
基金Project supported by the National Natural Science Foundation of China, No. 39500138
文摘INTRODUCTIONLiver fibrosis is a dynamic course leading tocirrhosis from a various chronic liver diseases. Thepathological basis of fibrosis is the disturbance ofproduction and degradation of the extracellularmatrix (ECM), which causes accumulation of ECMin the liver[1,2].
基金supported by National Natural Science Foundation of China (GrantNo. 60672160)the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001)+3 种基金the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (Grant No. 09YZ13)the Netherlands Organization for Scientific Research (NWO)Singapore MoE Tier 1 Research Grant RG60/07Shanghai Leading Academic Discipline Project (Grant No. J50101)
文摘We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.
文摘We know matrices and their transposes and we also know flip matrices. In my previous paper <i>Matrices-One Review</i>, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would like to introduce water image of four matrices said above and properties of such matrices. Also we know, determinant of sum of matrices is not equal to sum of determinant of matrices. Why can’t we get equal value on addition side and additive side of determinant of matrix addition and subtraction? This question triggered me to find the reason. The basic algebra of mensuration gave ideas to retreat determinant of matrix addition and subtraction. I extent that ideas for matrices sum. Further, in 1812, French mathematician <b>Jacques Philippe Marie Binet</b> described how to multiply matrices. Matrices are defined on addition, subtraction and multiplication but not in division. By the inspiration of Binet, I would like to describe how to do divisions on matrices. This idea is derived from division of fractions. In division of fraction, reciprocal of divisor fraction multiplies with dividend fraction. I do the same in division on matrices with some modifications. By this way, we could find quotient matrix and remainder matrix which satisfy division algorithm. So we could say, determinant of division of dividend matrix and divisor matrix is equal to division of determinant of dividend matrix and determinant of divisor matrix.
