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Minimum rank of skew-symmetric matrices described by a graph
North Holland [etc.] 2010 Linear algebra and its applications Vol.432 No.10
The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i<>j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied extensively. We define the minimum skew rank of a simple graph G to be the smallest possible rank among all skew-symmetric matrices over F whose ijth entry (for i<>j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We apply techniques from the minimum (symmetric) rank problem and from skew-symmetric matrices to obtain results about the minimum skew rank problem.
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Shailesh K. Bhavsar,Chaitanya G. Joshi,Dharamshibhai N. Rank,Aswin M. Thaker,Harshad V.Goriya,Anil Kalia 대한수의학회 2005 Journal of Veterinary Science Vol.6 No.4
The present work was to study induction of cytochrome P450 (CYP)3A and CYP2H1 gene by reverse transcriptase polymerase chain reaction (RT-PCR) and quantitative RTPCR in Bantam, Bantamized White Leghorn and White Leghorn chicks. Out of 18 chicks total 3 from each group (Bantam, Bantamized White Leghorn and White Leghorn) were treated intraperitoneal with phenobarbital at the dose rate of 12 mg/100 g (body weight) while the control group was treated with the saline. Total RNA was extracted from the liver samples using Tri Reagent based method. First strand cDNA was synthesized using one step RT-PCR kit. The PCR was performed and the product was subjected to agarose gel electrophoresis. Quantitative RT-PCR was conducted to quantify gene expression level of CYP3A and CYP2H1 genes. Relative expression ratio of CYP3A and CYP2H1 genes was calculated using relative expression software tool (REST). It was found that CYP3A is up regulated by factor of 1.34,14.51 and 1.00 in Bantam, Bantamized White Leghorn and White Leghorn chicks, respectively. In Bantam and Bantamized White Leghorn chicks CYP2H1 gene was up regulated by factor 1.50 and 80.87, respectively but down regulated by a factor of 1.97 in White Leghorn chicks. The PCR efficiency ranged from 1.30 to 1.70, 0.86 to 1.70 and 0.91 to 1.58 for CYP3A, CYP2H1 and β-actin, respectively in Bantam, Bantamized White Leghorn and White Leghorn chicks.
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Bhatt, Vaibhav D.,Khade, Prasad S.,Tarate, Sagar B.,Tripathi, Ajai K.,Nauriyal, Dev S.,Rank, Dharamshi N.,Kunjadia, Anju P.,Joshi, Chaitanya G. The Korean Society of Veterinary Science 2012 大韓獸醫學會誌 Vol.52 No.4
The expression profiles of inflammatory cytokines viz. interleukins (IL)-6, IL-8, IL-12, granulocyte macrophage-colony stimulating factor, interferon-${\gamma}$ and tumor necrosis factor-${\alpha}$ in response to subclinical mastitis in indigenous cattle breed Kankrej (n = 6), Gir (Bos indicus) (n = 12) and crossbred (Bos taurus${\times}$Bos indicus) (n = 7) were investigated using quantitative real time PCR. Significant correlation (p < 0.05) was observed between total bacterial load and somatic cell count (SCC) in all three breeds of cattle. All the cytokines were observed to be up-regulated compared to cows with healthy quarters, however, level of their expression varied among three breeds of cattle. In Kankrej most cytokines were found to be transcribed to higher levels than in other two breeds; the milk had higher load of bacteria but not so high SCC, implying that Kankrej has a higher inherent resistance against mastitis. The results of present study indicated that mammary glands of crossbred cattle are more sensitive to bacterial infection than indigenous breed of cattle as they elicit immune response at lower bacterial load and result into higher SCC. Research on identification of factors responsible for differentially expressed cytokines profiles and use of cytokines as immunomodulatory tools can pave way for formulating control strategies against bovine mastitis.
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