Inference of Probabilities over a Stochastic IL-System by Quantifier Elimination |
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Authors: | Hiroshi Yoshida Katsuhisa Horimoto Hirokazu Anai |
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Institution: | (1) Faculty of Mathematics, Organization for the Promotion of Advanced Research, Kyushu University, Hakozaki 6–10–1, Higashi-ku, Fukuoka 812–8581, Japan;(2) Computational Biology Research Centre (CBRC), National Institute of Advanced Industrial Science and Technology (AIST), Aomi 2–42, Koto-ku, Tokyo 135–0064, Japan;(3) IT Core Laboratories, Fujitsu Laboratories Ltd./CREST, JST., Kamikodanaka 4–1–1, Nakahara-ku, Kawasaki 211–8588, Japan |
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Abstract: | 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.
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Keywords: | 03C10 62M99 65H10 03D05 |
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