96,412 research outputs found
Random Boolean Networks
This review explains in a self-contained way the properties of random Boolean
networks and their attractors, with a special focus on critical networks. Using
small example networks, analytical calculations, phenomenological arguments,
and problems to solve, the basic concepts are introduced and important results
concerning phase diagrams, numbers of relevant nodes and attractor properties
are derived.Comment: This is a review on Random Boolean Networks. The new version now
includes a proper title page. The main body is unchange
Symmetry in Critical Random Boolean Network Dynamics
Using Boolean networks as prototypical examples, the role of symmetry in the
dynamics of heterogeneous complex systems is explored. We show that symmetry of
the dynamics, especially in critical states, is a controlling feature that can
be used both to greatly simplify analysis and to characterize different types
of dynamics. Symmetry in Boolean networks is found by determining the frequency
at which the various Boolean output functions occur. There are classes of
functions that consist of Boolean functions that behave similarly. These
classes are orbits of the controlling symmetry group. We find that the symmetry
that controls the critical random Boolean networks is expressed through the
frequency by which output functions are utilized by nodes that remain active on
dynamical attractors. This symmetry preserves canalization, a form of network
robustness. We compare it to a different symmetry known to control the dynamics
of an evolutionary process that allows Boolean networks to organize into a
critical state. Our results demonstrate the usefulness and power of using the
symmetry of the behavior of the nodes to characterize complex network dynamics,
and introduce a novel approach to the analysis of heterogeneous complex
systems
Response of Boolean networks to perturbations
We evaluate the probability that a Boolean network returns to an attractor
after perturbing h nodes. We find that the return probability as function of h
can display a variety of different behaviours, which yields insights into the
state-space structure. In addition to performing computer simulations, we
derive analytical results for several types of Boolean networks, in particular
for Random Boolean Networks. We also apply our method to networks that have
been evolved for robustness to small perturbations, and to a biological
example
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