A circuit-preserving mapping from multilevel to Boolean dynamics.

@article{Faur2018ACM,
  title={A circuit-preserving mapping from multilevel to Boolean dynamics.},
  author={Adrien Faur{\'e} and Shizuo Kaji},
  journal={Journal of theoretical biology},
  year={2018},
  volume={440},
  pages={
          71-79
        }
}

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References

SHOWING 1-10 OF 25 REFERENCES
Mapping multivalued onto Boolean dynamics.
On the conversion of multivalued gene regulatory networks to Boolean dynamics
TLDR
The modeling approach introduced by R. Thomas for the qualitative study of gene regulatory networks is considered, and a Boolean map is created showing that, for $n \geq 6$, the absence of fixed points is compatible with the presence of local negative circuits in the regulatory graph.
On Circuit Functionality in Boolean Networks
TLDR
Focusing on Boolean networks, some definitions concerning the notion of functionality are recalled and proposed and some results are proposed along with associated mathematical results.
Continuous time boolean modeling for biological signaling: application of Gillespie algorithm
TLDR
An algorithm for modeling biological networks in a discrete framework with continuous time based on continuous time Markov process applied on a Boolean state space, which allows to describe kinetic phenomena which were difficult to handle in the original models.
Polynomial algebra of discrete models in systems biology
TLDR
A unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets can be provided, which allows the use of a variety of mathematical tools from computer algebra for their analysis.
Minimization and equivalence in multi-valued logical models of regulatory networks
TLDR
This work studies the conditions allowing for such effects by analysing classes of dynamically equivalent models and both structurally maximal and minimal representatives of such classes and presents an efficient algorithm that constructs a minimal representative of the respective class of a given multi-valued model.
Logical Modeling and Dynamical Analysis of Cellular Networks
TLDR
A number of recent methodological advances to ease the analysis of large and intricate networks are reviewed, including approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models.
State–time spectrum of signal transduction logic models
TLDR
An overview of logic modeling formalisms in the context of training logic models to data is presented, and specifically the different approaches to modeling qualitative to quantitative data (state) and dynamics (time) of signal transduction are presented.
A description of dynamical graphs associated to elementary regulatory circuits
TLDR
It is shown that the structure of synchronous and asynchronous dynamical graphs depends only on the length of the circuit and on its sign, which constitutes a first step towards the analytical characterisation of discrete dynamical graph for more complex regulatory networks in terms of contributions corresponding to their embedded elementary circuits.
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