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THE PERIODIC JACOBI MATRIX PROCRUSTES PROBLEM
Li, Jiao-Fen,Hu, Xi-Yan The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
The following "Periodic Jacobi Procrustes" problem is studied: find the Periodic Jacobi matrix X which minimizes the Frobenius (or Euclidean) norm of AX - B, with A and B as given rectangular matrices. The class of Procrustes problems has many application in the biological, physical and social sciences just as in the investigation of elastic structures. The different problems are obtained varying the structure of the matrices belonging to the feasible set. Higham has solved the orthogonal, the symmetric and the positive definite cases. Andersson and Elfving have studied the symmetric positive semidefinite case and the (symmetric) elementwise nonnegative case. In this contribution, we extend and develop these research, however, in a relatively simple way. Numerical difficulties are discussed and illustrated by examples.
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THE PERIODIC JACOBI MATRIX PROCRUSTES PROBLEM
Jiao-fen Li,XI-YAN HU 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
The following ”Periodic Jacobi Procrustes” problem is stud-ied: find the Periodic Jacobi matrix X which minimizes the Frobenius (or Euclidean) norm of AX −B, with A and B as given rectangular matrices. The class of Procrustes problems has many application in the biological,physical and social sciences just as in the investigation of elastic struc-tures. The different problems are obtained varying the structure of the matrices belonging to the feasible set. Higham has solved the orthogonal,the symmetric and the positive definite cases. Andersson and Elfving have studied the symmetric positive semidefinite case and the (symmetric) el-ementwise nonnegative case. In this contribution, we extend and develop these research, however, in a relatively simple way. Numerical difficulties are discussed and illustrated by examples.
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( Weitao Shen ),( Jiayu Sun ),( Zhiyang Li ),( Fen Yao ),( Kaihuang Lin ),( Xiaoyang Jiao ) 대한내과학회 2021 The Korean Journal of Internal Medicine Vol.36 No.3
Background/Aim: It is known that an imbalance in the intestinal f lora plays a crucial role in colorectal cancer (CRC), but the effect of food consumption pat terns on the types of intestinal flora remains to be clarified. We aimed to analyze the associations between food intake and intestinal flora in healthy and CRC indi viduals. Methods: Food intake data were recorded using the Food Frequency Question naire (FFQ). The composition and diversity of the intestinal flora detected by 16S rRNA gene sequencing, and the data were analyzed by R version 3.1.1 software. Results: Higher intake of red meat or pickled foods, and lower intake of white meat, fruits, vegetables, beans, nuts were found in the CRC group compared with the healthy group. Higher levels of Fusobacteria and Proteobacteria, and lower levels of Firmicutes were observed in the CRC group. Partial correlation analysis revealed that the intake of fruits, beans, and nuts was negatively correlated with Proteobac teria and Fusobacteria, but pickled food was positively correlated with Fusobacteria (p < 0.05). Fish, beans, and nuts intake was negatively correlated with Escherichia (p = 0.01). Multiple regression analysis revealed that vegetable oil (odds ratio [OR], 0.26; 95% confidence interval [CI], 0.13 to 0.82), vegetables (OR, 0.26; 95% CI, 0.10 to 0.64), eggs (OR, 0.26; 95% CI, 0.10 to 0.69), pickled foods (OR, 21.02; 95% CI, 6.02 to 73.45), and red meat (OR, 4.23; 95% CI, 1.68 to 10.60) had an impact on CRC risk. Conclusions: The species and abundance of intestinal flora varies between CRC and healthy individuals and may be affected by their food preference.
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