Inference of probabilities over a stochastic IL-system by quantifier elimination

Hiroshi Yoshida, Katsuhisa Horimoto, Hirokazu Anai

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    An algebraic approach based on quantifier elimination is proposed for the inference of probabilistic parameters over stochastic Lindenmayer systems with interaction, IL-systems. We are concerned with a multi-cellular organism as an instance of a stochastic IL system. The organism starts with one or a few cells, and develops different types of cells with distinct functions. We have constructed a simple model with cell-type order conservation and have assessed conditions for high cell-type diversity. This model is based on the stochastic IL-system for three types of cells. The cell-type order conservation corresponds to interaction terms in the IL-system. In our model, we have successfully inferred algebraic relations between the probabilities for cell-type diversity by using a symbolic method, quantifier elimination (QE). Surprisingly, three modes for the proliferation and transition rates emerged for various ratios of the initial cells to the developed cells. Furthermore, we have found that the high cell-type diversity pattern originates from the cell-type order conservation. Thus, QE has yielded analysis of the IL-system, which has revealed that, during the developing process of multi-cellular organisms, complex but explicit relations exist between cell-type diversity patterns and developmental rates.

    Original languageEnglish
    Pages (from-to)473-485
    Number of pages13
    JournalMathematics in Computer Science
    Issue number3
    Publication statusPublished - Mar 2008

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Computational Theory and Mathematics
    • Applied Mathematics


    Dive into the research topics of 'Inference of probabilities over a stochastic IL-system by quantifier elimination'. Together they form a unique fingerprint.

    Cite this