Algebraic Approaches to Underdetermined Experiments in Biology

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概要

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• 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.

• 2010-09-14

著者

• Hiroshi Yoshida

  Kyushu University

• Kinji Kimura

  Kyoto University

• Naoki Yoshida

  University of Tsukuba

• Junko Tanaka

  University of Tsukuba

• Yoshihiro Miwa

  University of Tsukuba

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