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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 209
Probabilistic Regulatory Networks: Modelling Genetic Networks M.A. Avino-Diaz1 and O. Moreno2
1Department of Mathematic-Physics, Cayey,
Full Bibliographic Reference for this paper
M.A. Avino-Diaz, O. Moreno, "Probabilistic Regulatory Networks: Modelling Genetic Networks", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 209, 2006. doi:10.4203/ccp.84.209
Keywords: isomorphism of Markov chain, probabilistic regulatory networks, Boolean network, transition matrix, category, dynamical systems.
Summary
We can understand the complex interactions of genes
using simplified models, such as discrete or continuous models of
genes. Developing computational tools permits description of gene
functions and understanding the mechanism of regulation
[3]. We focus our attention in the discrete structure of
genetic regulatory networks instead of continuous models.
The probabilistic gene regulatory network (PRN) is a natural
generalization of the probabilistic boolean network (PBN) model
introduced in [4,1]. This model has n
functions defined over a finite set X to itself, with
probabilities assigned to these functions. We present here the ideas
of
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If
For example: suppose we have
two genes with two values that we denote as usual
A mathematical method is constructed here given the dependency graph
of a set of genes. These genes could have either two, or three values.
The model that we obtain gives the
information about the subnetworks, the possible projections, and
the fixed points. We present here a methodology for construct discrete
networks using the dependency graph and a time series data.
For genes with more than two states, we assign three
possible values References
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