Narrow Results

In previous work, the limit structure of positive and negative finite threshold boolean networks without inputs (TBNs) over the complete digraph K_n was analyzed and an algorithm was presented for computing this structure in polynomial time. Those results are generalized in this paper to cover the case of arbitrary TBNs over K_n. Although the limit structure is now more complicated, containing, not only fixed-points and cycles of length 2, but possibly also cycles of arbitrary length, a simple algorithm is still available for its determination in polynomial time. Finally, the algorithm is generalized to cover the case of symmetric finite boolean networks over K_n.

Our numerical simulation first displays exponential increase of the mean number of attractors with N for K = 2,3,4 and 50≦ N ≦350. The mean length of attractors also increases exponentially with N for K = 2, but increases linearly with N for K = 3,4. We further found the larger the K the larger S/N value; which yields the results that the mean length and the mean number of attractors of critical random Boolean networks will decrease with larger K.

Evolution of cooperation has attracted considerable attention but so far no definitive answer exists. Probably each kind of problem has specific answers. This paper deals with evolution of cooperation in public goods games. We use random Boolean networks to formalize the non-local influence of K agents over a given agent. This formalism allows the representation of a variety of network regulation mechanisms by means of (i) different topologies and (ii) Boolean functions that do the regulation proper. However, random functions and connections do not necessarily lead to cooperation. Thus, it is necessary to find what kind of network structure is prone to promote cooperation. We employ an evolutionary approach to show that evolving the topologies and the random functions leads to much fitter structures.

Random Boolean networks provide a way to give a precise meaning to the notion that living beings are in a critical state. Some phenomena which are observed in real biological systems (distribution of "avalanches" in gene knock-out experiments) can be modeled using random Boolean networks, and the results can be analytically proven to depend upon the Derrida parameter, which also determines whether the network is critical. By comparing observed and simulated data one can then draw inferences about the criticality of biological cells, although with some care because of the limited number of experimental observations. The relationship between the criticality of a single network and that of a set of interacting networks, which simulate a tissue or a bacterial colony, is also analyzed by computer simulations.

In this paper we investigate how the dynamics of a set of coupled Random Boolean Netowrks is affected by the changes in their topology. The Multi Random Boolean Networks (MRBN) is a model for the interaction among Random Boolean Networks (RBN). A single RBN may be regarded as an abstraction of gene regulatory networks, thus MRBNs might represent collections of communicating cells e.g. in tissues or in bacteria colonies. Past studies have shown how the dynamics of classical RBNs in the critical regime is affected by such an interaction. Here we compare the behaviour of RBNs with random topology to that of RBNs with scale-free topology for different dynamical regimes.

In this work we simulate gene knock-out experiments in networks in which variable domains are continuous and variables can vary continuously in time. This model is more realistic than other well-known switching networks such as Boolean Networks. We show that continuous networks can reproduce the results obtained by Random Boolean Networks (RBN). Nevertheless, they do not reproduce the whole range of activation values of actual experimental data. The reasons for this behavior very close to that of RBN could be found in the specific parameter setting chosen and lines for further investigation are discussed.

Recent works have shown that the model of random Boolean networks, properly modified in order to take into account the influence of random fluctuations, can describe a set of phenomena which are related to cell differentiation. The main results are summarized here, and the methodological implications of this kind of models are discussed.