## 8 Citations

On the conversion of multivalued gene regulatory networks to Boolean dynamics

- Mathematics, Computer ScienceArXiv
- 2017

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.

Graph properties of biological interaction networks

- Computer Science
- 2018

It is shown how regulatory properties of Boolean networks can be investigated via satisfiability problems, and used to examine the role of local negative circuits in networks of small dimension, and proposes algorithms for elimination of intermediate species that can be used to find whether a mass action network simplifies to a given chemical system.

Local negative circuits and cyclic attractors in Boolean networks with at most five components

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2019

It is shown that the question on the relationship between the asymptotic behaviours of Boolean networks and their regulatory structures: does the presence of a cyclic attractor imply the existence of a local negative circuit in the regulatory graph can be translated into a Boolean satisfiability problem on n variables.

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

- Computer ScienceEntropy
- 2021

An update to PyPhi is presented that extends its applicability to systems constituted of discrete, but multi-valued elements and applies the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2).

Positive and negative cycles in Boolean networks

- Computer ScienceJournal of theoretical biology
- 2019

Bisimilar Conversion of Multi-valued Networks to Boolean Networks

- Computer ScienceArXiv
- 2020

This article investigates the bisimilar conversion where the Boolean integer coding is a parameter that can be freely modified and defines a computational method automatically inferring a bisimilar Boolean network from a given Multi-valued one.

## References

SHOWING 1-10 OF 25 REFERENCES

Mapping multivalued onto Boolean dynamics.

- Computer ScienceJournal of theoretical biology
- 2011

On the conversion of multivalued gene regulatory networks to Boolean dynamics

- Mathematics, Computer ScienceArXiv
- 2017

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

- Computer Science, MathematicsBulletin of mathematical biology
- 2013

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.

Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework

- MathematicsAdv. Appl. Math.
- 2008

Continuous time boolean modeling for biological signaling: application of Gillespie algorithm

- Computer Science, BiologyBMC Systems Biology
- 2012

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

- Computer ScienceBioinform.
- 2010

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

- Computer ScienceNatural Computing
- 2015

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

- Biology, Computer ScienceFront. Genet.
- 2016

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

- Computer SciencePhysical biology
- 2012

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

- Computer ScienceECCB
- 2003

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.