Algebraic approaches to underdetermined experiments in biology

Hiroshi Yoshida, Kinji Kimura, Naoki Yoshida, Junko Tanaka, Yoshihiro Miwa

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    1 Citation (Scopus)


    We sometimes meet an experiment in which its rate constants cannot be determined in this experiment only; in this case, it is called an underdetermined experiment. One of methods to overcome underdetermination is to combine results of multiple experiments. Multiple experiments give rise to a large number of parameters and variables to analyze, and usually even have a complicated solution with multiple solutions, which situation is unknown to us beforehand. These two difficulties: underdetermination and multiple solutions, lead to confusion as to whether rate constants can intrinsically be determined through experiment or not. In order to analyze such experiments, we use 'prime ideal decomposition' to decompose a solution into simpler solutions. It is, however, hard to decompose a set of polynomials with a large number of parameters and variables. Exemplifying a bio-imaging problem, we propose one tip and one technique using 'resultant' from a biological viewpoint.

    Original languageEnglish
    Pages (from-to)62-69
    Number of pages8
    JournalIPSJ Transactions on Bioinformatics
    Publication statusPublished - 2010

    All Science Journal Classification (ASJC) codes

    • Biochemistry, Genetics and Molecular Biology (miscellaneous)
    • Computer Science Applications


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