Characterizing short-term stability for Boolean networks over any distribution of transfer functions

@article{Seshadhri2016CharacterizingSS,
  title={Characterizing short-term stability for Boolean networks over any distribution of transfer functions},
  author={C. Seshadhri and Andrew M. Smith and Yevgeniy Vorobeychik and Jackson Mayo and Robert C. Armstrong},
  journal={Physical review. E},
  year={2016},
  volume={94 1-1},
  pages={
          012301
        }
}
We present a characterization of short-term stability of Kauffman's NK (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of this formula is the Fourier analysis of Boolean functions, which describes such functions as… 

Figures from this paper

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology.

TLDR
It is proved that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition.

Testing Phase Space Properties of Synchronous Dynamical Systems with Nested Canalyzing Local Functions

TLDR
This work studies a variety of analysis problems for synchronous graphical dynamical systems (SyDSs) over the Boolean domain, where each local function is an NCF, and presents intractability results for some properties as well as efficient algorithms for others.

Phase transitions and assortativity in models of gene regulatory networks evolved under different selection processes

TLDR
It is found that when selection depends only on structure, evolved networks are resistant to widespread damage propagation, even without knowledge of individual gene propensities for becoming ‘damaged’.

Diagrammatic expansion of information flows in stochastic Boolean networks

TLDR
The authors develop a diagrammatic expansion to compute transfer entropy in stochastic Boolean networks analytically and demonstrate the power of the explicit specification of a discrete-time model.

Using computational game theory to guide verification and security in hardware designs

TLDR
The defender's strategy in equilibrium is interpreted as a prioritization of the allocation of verification resources in the presence of an adversary, which is applied to synthesized hardware implementations using the design's network structure and logic to inform defender valuations and verification costs.

Random Boolean Networks as a toy model for the brain

TLDR
The connectivity matrix describing the strength of the connection between two nodes is structured following biological statements such as Dale’s principle and the balance between excitatory and inhibitory nodes; departure from the Gaussian distribution is also explored.

References

SHOWING 1-10 OF 29 REFERENCES

Influence and Dynamic Behavior in Random Boolean Networks

TLDR
This work uses a rigorous mathematical framework to provide the first formal proof of many of the standard critical transition results in boolean network analysis, and offers analogous characterizations for novel classes of random boolean networks.

Stability of Boolean networks: the joint effects of topology and update rules.

TLDR
Numerical simulations confirm the theory and show that local correlations between topology and update rules can have profound effects on the qualitative behavior of these systems.

Activities and sensitivities in boolean network models.

TLDR
In a random Boolean network, it is shown that the expected average sensitivity determines the well-known critical transition curve and the important role of the average sensitivity in determining the dynamical behavior of a Boolean network is demonstrated.

The role of certain Post classes in Boolean network models of genetic networks

TLDR
It is demonstrated that networks constructed from functions belonging to classes of Boolean functions that are closed under composition have a tendency toward ordered behavior, and are not overly sensitive to initial conditions, and damage does not readily spread throughout the network.

Dynamics of Boolean networks: an exact solution.

TLDR
A general formulation, suitable for BN with any distribution of Boolean functions, is developed and provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology.

Harmonic analysis of Boolean networks: determinative power and perturbations

TLDR
It is argued that the mutual information (MI) between a given subset of the inputs X={X1,...,Xn} of some node i and its associated function fi(X) quantifies the determinative power of this set of inputs over node i.

Genetic networks with canalyzing Boolean rules are always stable.

TLDR
The results indicate that for single cells, the dynamics should become more stable with evolution, and there are hints that genetic networks acquire broader degree distributions with evolution.

Noisy random Boolean formulae: a statistical physics perspective.

TLDR
Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology and the framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used.

Boolean Threshold Networks: Virtues and Limitations for Biological Modeling

TLDR
Only for a very restricted set of parameters, Kauffman Boolean networks show dynamical properties consistent with what is observed in biological systems, and the virtues of these properties and the possible problems related with the restrictions are discussed.