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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Boolean network | 2/2 | https://en.wikipedia.org/wiki/Boolean_network | reference | science, encyclopedia | 2026-05-05T14:01:56.694067+00:00 | kb-cron |
q
i
=
2
p
i
(
1
−
p
i
)
{\displaystyle q_{i}=2p_{i}(1-p_{i})}
. In the general case, stability of the network is governed by the largest eigenvalue
λ
Q
{\displaystyle \lambda _{Q}}
of matrix
Q
{\displaystyle Q}
, where
Q
i
j
=
q
i
A
i
j
{\displaystyle Q_{ij}=q_{i}A_{ij}}
, and
A
{\displaystyle A}
is the adjacency matrix of the network. The network is stable if
λ
Q
<
1
{\displaystyle \lambda _{Q}<1}
, critical if
λ
Q
=
1
{\displaystyle \lambda _{Q}=1}
, unstable if
λ
Q
>
1
{\displaystyle \lambda _{Q}>1}
.
== Variations of the model ==
=== Other topologies === One theme is to study different underlying graph topologies.
The homogeneous case simply refers to a grid which is simply the reduction to the famous Ising model. Scale-free topologies may be chosen for Boolean networks. One can distinguish the case where only in-degree distribution in power-law distributed, or only the out-degree-distribution or both.
=== Other updating schemes === Classical Boolean networks (sometimes called CRBN, i.e. Classic Random Boolean Network) are synchronously updated. Motivated by the fact that genes don't usually change their state simultaneously, different alternatives have been introduced. A common classification is the following:
Deterministic asynchronous updated Boolean networks (DRBNs) are not synchronously updated but a deterministic solution still exists. A node i will be updated when t ≡ Qi (mod Pi) where t is the time step. The most general case is full stochastic updating (GARBN, general asynchronous random Boolean networks). Here, one (or more) node(s) are selected at each computational step to be updated. The Partially-Observed Boolean Dynamical System (POBDS) signal model differs from all previous deterministic and stochastic Boolean network models by removing the assumption of direct observability of the Boolean state vector and allowing uncertainty in the observation process, addressing the scenario encountered in practice. Autonomous Boolean networks (ABNs) are updated in continuous time (t is a real number, not an integer), which leads to race conditions and complex dynamical behavior such as deterministic chaos.
== Application of Boolean Networks ==
=== Classification === The Scalable Optimal Bayesian Classification developed an optimal classification of trajectories accounting for potential model uncertainty and also proposed a particle-based trajectory classification that is highly scalable for large networks with much lower complexity than the optimal solution.
== See also == NK model
== References ==
Dubrova, E., Teslenko, M., Martinelli, A., (2005). *Kauffman Networks: Analysis and Applications, in "Proceedings of International Conference on Computer-Aided Design", pages 479-484.
== External links == Analysis of Dynamic Algebraic Models (ADAM) v1.1 bioasp/bonesis: Synthesis of Most Permissive Boolean Networks from network architecture and dynamical properties CoLoMoTo (Consortium for Logical Models and Tools) DDLab NetBuilder Boolean Networks Simulator Open Source Boolean Network Simulator JavaScript Kauffman Network Probabilistic Boolean Networks (PBN) RBNLab A SAT-based tool for computing attractors in Boolean Networks