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

The naturalness in the BLMSSM and B-LSSM

In order to interpret the Higgs mass and its decays more naturally, we hope to intrude the BLMSSM and B-LSSM. In the both models, the right-handed neutrino superfields are introduced to better explain the neutrino mass problems. In addition, there are other superfields considered to make these models more natural than MSSM. In this paper, the method of $\chi^2$ analyses will be adopted in the BLMSSM and B-LSSM to calculate the Higgs mass, Higgs decays and muon $g-2$. With the fine-tuning in the region $0.67\%-2.5\%$ and $0.67\%-5\%$, we can obtain the reasonable theoretical values that are in accordance with the experimental results respectively in the BLMSSM and B-LSSM. Meanwhile, the best-fitted benchmark points in the BLMSSM and B-LSSM will be acquired at minimal $(\chi^{BL}_{min})^2 = 2.34736$ and $(\chi^{B-L}_{min})^2 = 2.47754$, respectively

The order analysis for the two loop corrections to lepton MDM

The experimental data of the magnetic dipole moment(MDM) of lepton($e$, $\mu$) is very exact. The deviation between the experimental data and the standard model prediction maybe come from new physics contribution. In the supersymmetric models, there are very many two loop diagrams contributing to the lepton MDM. In supersymmetric models, we suppose two mass scales $M_{SH}$ and $M$ with $M_{SH}\gg M$ for supersymmetric particles. Squarks belong to $M_{SH}$ and the other supersymmetric particles belong to $M$. We analyze the order of the contributions from the two loop diagrams. The two loop triangle diagrams corresponding to the two loop self-energy diagram satisfy Ward-identity, and their contributions possess particular factors. This work can help to distinguish the important two loop diagrams giving corrections to lepton MDM.Comment: 12 pages, 3 figure

Dry computational approaches for wet medical problems

This is a report on the 4th international conference in ‘Quantitative Biology and Bioinformatics in Modern Medicine’ held in Belfast (UK), 19–20 September 2013. The aim of the conference was to bring together leading experts from a variety of different areas that are key for Systems Medicine to exchange novel findings and promote interdisciplinary ideas and collaborations