A statistical framework for the design of microarray experiments and effective detection of differential gene expression

Four reasons why you might wish to read this paper: 1. We have devised a new statistical T test to determine differentially expressed genes (DEG) in the context of microarray experiments. This statistical test adds a new member to the traditional T-test family. 2. An exact formula for calculating the detection power of this T test is presented, which can also be fairly easily modified to cover the traditional T tests. 3. We have presented an accurate yet computationally very simple method to estimate the fraction of non-DEGs in a set of genes being tested. This method is superior to an existing one which is computationally much involved. 4. We approach the multiple testing problem from a fresh angle, and discuss its relation to the classical Bonferroni procedure and to the FDR (false discovery rate) approach. This is most useful in the analysis of microarray data, where typically several thousands of genes are being tested simultaneously.Comment: 9 pages, 1 table; to appear in Bioinformatic

A Sharp upper bound for the spectral radius of a nonnegative matrix and applications

In this paper, we obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of a graph or a digraph. These results are new or generalize some known results.Comment: 16 pages in Czechoslovak Math. J., 2016. arXiv admin note: text overlap with arXiv:1507.0705