Abstract
Complex system theory deals with dynamical systems containing a very large number of variables. The resulting dynamical behavior can be arbitrary complex and sophisticated. It is therefore important to have well controlled benchmarks, dynamical systems which can be investigated and understood in a controlled way for large numbers of variables. Networks of interacting binary variables, i.e. Boolean networks, constitute such canonical complex dynamical system. They allow the formulation and investigation of important concepts like phase transition in the resulting dynamical state. They are also recognized to be the starting points for the modeling of gene expression and protein regulation networks; the fundamental networks at the basis of all life.
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Notes
- 1.
Magnetic moments often have only two possible directions (up or down in the language of spin-1/2 particles). A compound is hence magnetic when more moments point into one of the two possible directions, viz if the two directions are populated unequally.
- 2.
An alloy made up of two or more substances is said to be “quenched” when it is cooled so quickly that it remains stuck in a specific atomic configuration, which does not change anymore with time.
- 3.
A compound is said to be “annealed” when it has been kept long enough at elevated temperatures such that the thermodynamic stable configuration has been achieved.
- 4.
Genes are boolean variables in the sense that they are either expressed or not. The quantitative amount of proteins produced by a given active gene is regulated via a separate mechanism involving microRNA, small RNA snippets.
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Gros, C. (2015). Random Boolean Networks. In: Complex and Adaptive Dynamical Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-16265-2_7
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