We analyzed global gene expression in Arabidopsis in response to various hormones and in related experiments as part of the AtGenExpress project. The experimental agents included seven basic phytohormones (auxin, cytokinin, gibberellin, brassinosteroid, abscisic acid, jasmonate and ethylene) and their inhibitors. In addition, gene expression was investigated in hormone-related mutants and during seed germination and sulfate starvation. Hormone-inducible genes were identified from the hormone response data. The effects of each hormone and the relevance of the gene lists were verified by comparing expression profiles for the hormone treatments and related experiments using Pearson's correlation coefficient. This approach was also used to analyze the relationships among expression profiles for hormone responses and those included in the AtGenExpress stress-response data set. The expected correlations were observed, indicating that this approach is useful to monitor the hormonal status in the stress-related samples. Global interactions among hormones-inducible genes were analyzed in a pairwise fashion, and several known and novel hormone interactions were detected. Genome-wide transcriptional gene-to-gene correlations, analyzed by hierarchical cluster analysis (HCA), indicated that our data set is useful for identification of clusters of co-expressed genes, and to predict the functions of unknown genes, even if a gene's function is not directly related to the experiments included in AtGenExpress. Our data are available online from AtGenExpressJapan; the results of genome-wide HCA are available from PRIMe. The data set presented here will be a versatile resource for future hormone studies, and constitutes a reference for genome-wide gene expression in Arabidopsis.

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A contour integral method is proposed to solve nonlinear eigenvalue problems numerically. The target equation is F (λ)x = 0, where the matrix F (λ) is an analytic matrix function of λ. The method can extract only the eigenvalues λ in a domain defined by the integral path, by reducing the original problem to a linear eigenvalue problem that has identical eigenvalues in the domain. Theoretical aspects of the method are discussed, and we illustrate how to apply of the method with some numerical examples.

The Sakurai-Sugiura projection method, which solves a generalized eigenvalue problem to find certain eigenvalues in a given domain, was reformulated by using the resolvent theory. A new interpretation based on the filter diagonalization was given, and the corresponding filter function was derived explicitly. The block version of the method was also proposed, which enabled to resolve degenerated eigenvalues. Two numerical examples were provided to illustrate the method.

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