High Dimensional Multivariate Inference Under General Conditions

In this dissertation, we investigate four distinct and interrelated problems for high-dimensional inference of mean vectors in multi-groups. The first problem concerned is the profile analysis of high dimensional repeated measures. We introduce new test statistics and derive its asymptotic distribution under normality for equal as well as unequal covariance cases. Our derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. We also derive consistent and unbiased estimators of the asymptotic variances for equal and unequal covariance cases respectively. The second problem considered is the accurate inference for high-dimensional repeated measures in factorial designs as well as any comparisons among the cell means. We derive asymptotic expansion for the null distributions and the quantiles of a suitable test statistic under normality. We also derive the estimator of parameters contained in the approximate distribution with second-order consistency. The most important contribution is high accuracy of the methods, in the sense that p-values are accurate up to the second order in sample size as well as in dimension. The third problem pertains to the high-dimensional inference under non-normality. We relax the commonly imposed dependence conditions which has become a standard assumption in high dimensional inference. With the relaxed conditions, the scope of applicability of the results broadens. The fourth problem investigated pertains to a fully nonparametric rank-based comparison of high-dimensional populations. To develop the theory in this context, we prove a novel result for studying the asymptotic behavior of quadratic forms in ranks. The simulation studies provide evidence that our methods perform reasonably well in the high-dimensional situation. Real data from Electroencephalograph (EEG) study of alcoholic and control subjects is analyzed to illustrate the application of the results

Classification of Graded Left-symmetric Algebra Structures on Witt and Virasoro Algebras

We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebra structures on the Witt algebra are classified. All of them are simple and they include the examples given by Chapoton and Kupershmidt. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebra structures on the Virasoro algebra. They coincide with the examples given by Kupershmidt.Comment: 22 page

Accurate Inference for Repeated Measures in High Dimensions

This paper proposes inferential methods for high-dimensional repeated measures in factorial designs. High-dimensional refers to the situation where the dimension is growing with sample size such that either one could be larger than the other. The most important contribution relates to high-accuracy of the methods in the sense that p-values, for example, are accurate up to the second-order. Second-order accuracy in sample size as well as dimension is achieved by obtaining asymptotic expansion of the distribution of the test statistics, and estimation of the parameters of the approximate distribution with second-order consistency. The methods are presented in a unified and succinct manner that it covers general factorial designs as well as any comparisons among the cell means. Expression for asymptotic powers are derived under two reasonable local alternatives. A simulation study provides evidence for a gain in accuracy and power compared to limiting distribution approximations and other competing methods for high-dimensional repeated measures analysis. The application of the methods are illustrated with a real-data from Electroencephalogram (EEG) study of alcoholic and control subjects

Involvement of NADH Oxidase in Biofilm Formation in Streptococcus sanguinis

Biofilms play important roles in microbial communities and are related to infectious diseases. Here, we report direct evidence that a bacterial nox gene encoding NADH oxidase is involved in biofilm formation. A dramatic reduction in biofilm formation was observed in a Streptococcus sanguinis nox mutant under anaerobic conditions without any decrease in growth. The membrane fluidity of the mutant bacterial cells was found to be decreased and the fatty acid composition altered, with increased palmitic acid and decreased stearic acid and vaccenic acid. Extracellular DNA of the mutant was reduced in abundance and bacterial competence was suppressed. Gene expression analysis in the mutant identified two genes with altered expression, gtfP and Idh, which were found to be related to biofilm formation through examination of their deletion mutants. NADH oxidase-related metabolic pathways were analyzed, further clarifying the function of this enzyme in biofilm formation

Proteomics analysis of differentially expressed proteins in chicken trachea and kidney after infection with the highly virulent and attenuated coronavirus infectious bronchitis virus in vivo

<p>Abstract</p> <p>Background</p> <p>Infectious bronchitis virus (IBV) is first to be discovered coronavirus which is probably endemic in all regions with intensive impact on poultry production. In this study, we used two-dimensional gel electrophoresis (2-DE) and two-dimensional fluorescence difference gel electrophoresis (2-DIGE), coupled with matrix-assisted laser desorption/ionization time-of-flight tandem mass spectrometry (MALDI-TOF/TOF-MS), to explore the global proteome profiles of trachea and kidney tissues from chicken at different stages infected <it>in vivo </it>with the highly virulent ck/CH/LDL/97I P₅strain of infectious bronchitis virus (IBV) and the embryo-passaged, attenuated ck/CH/LDL/97I P₁₁₅strain.</p> <p>Results</p> <p>Fifty-eight differentially expressed proteins were identified. Results demonstrated that some proteins which had functions in cytoskeleton organization, anti-oxidative stress, and stress response, showed different change patterns in abundance from chicken infected with the highly virulent ck/CH/LDL/97I P₅strain and those given the embryo-passaged, attenuated P₁₁₅stain. In addition, the dynamic transcriptional alterations of 12 selected proteins were analyzed by the real-time RT-PCR, and western blot analysis confirmed the change in abundance of heat shock proteins (HSP) beta-1, annexin A2, and annexin A5.</p> <p>Conclusions</p> <p>The proteomic alterations described here may suggest that these changes to protein expression correlate with IBV virus' virulence in chicken, hence provides valuable insights into the interactions of IBV with its host and may also assist with investigations of the pathogenesis of IBV and other coronavirus infections.</p

Statistical inference of chromosomal homology based on gene colinearity and applications to Arabidopsis and rice

BACKGROUND: The identification of chromosomal homology will shed light on such mysteries of genome evolution as DNA duplication, rearrangement and loss. Several approaches have been developed to detect chromosomal homology based on gene synteny or colinearity. However, the previously reported implementations lack statistical inferences which are essential to reveal actual homologies. RESULTS: In this study, we present a statistical approach to detect homologous chromosomal segments based on gene colinearity. We implement this approach in a software package ColinearScan to detect putative colinear regions using a dynamic programming algorithm. Statistical models are proposed to estimate proper parameter values and evaluate the significance of putative homologous regions. Statistical inference, high computational efficiency and flexibility of input data type are three key features of our approach. CONCLUSION: We apply ColinearScan to the Arabidopsis and rice genomes to detect duplicated regions within each species and homologous fragments between these two species. We find many more homologous chromosomal segments in the rice genome than previously reported. We also find many small colinear segments between rice and Arabidopsis genomes

Identification of a novel linear B-cell epitope in the UL26 and UL26.5 proteins of Duck Enteritis Virus

BACKGROUND: The Unique Long 26 (UL26) and UL26.5 proteins of herpes simplex virus are known to function during the assembly of the viruses. However, for duck enteritis virus (DEV), which is an unassigned member of the family Herpesviridae, little information is available about the function of the two proteins. In this study, the C-terminus of DEV UL26 protein (designated UL26c), which contains the whole of UL26.5, was expressed, and the recombinant UL26c protein was used to immunize BALB/c mice to generate monoclonal antibodies (mAb). The mAb 1C8 was generated against DEV UL26 and UL26.5 proteins and used subsequently to map the epitope in this region. Both the mAb and its defined epitope will provide potential tools for further study of DEV. RESULTS: A mAb (designated 1C8) was generated against the DEV UL26c protein, and a series of 17 partially overlapping fragments that spanned the DEV UL26c were expressed with GST tags. These peptides were subjected to enzyme-linked immunosorbent assay (ELISA) and western blotting analysis using mAb 1C8 to identify the epitope. A linear motif, (520)IYYPGE(525), which was located at the C-terminus of the DEV UL26 and UL26.5 proteins, was identified by mAb 1C8. The result of the ELISA showed that this epitope could be recognized by DEV-positive serum from mice. The (520)IYYPGE(525 )motif was the minimal requirement for reactivity, as demonstrated by analysis of the reactivity of 1C8 with several truncated peptides derived from the motif. Alignment and comparison of the 1C8-defined epitope sequence with those of other alphaherpesviruses indicated that the motif (521)YYPGE(525 )in the epitope sequence was conserved among the alphaherpesviruses. CONCLUSION: A mAb, 1C8, was generated against DEV UL26c and the epitope-defined minimal sequence obtained using mAb 1C8 was (520)IYYPGE(525). The mAb and the identified epitope may be useful for further study of the design of diagnostic reagents for DEV