Random Boolean Network Model Research Articles

Coupled Analysis of Safety Risks in Bridge Construction Based on N-K Model and SNA

Bridge construction accidents are often caused by a variety of factors, so it is particularly important to explore the role mechanism of bridge construction accident risk factors to effectively prevent construction safety accidents and ensure the smooth construction of bridges. We collect the causes of bridge construction accidents in China from 2006 to 2023, take 126 typical cases as research samples, analyze the primary risk factors of bridge construction from four aspects (human factors, equipment factors, management factors, and environmental factors), establish a library of secondary risk factors with reference to the literature research, introduce the theory of risk coupling, and analyze the coupling mechanism and types of risk factors of bridge construction accidents. The N-K random Boolean network model (N-K model) quantifies the coupling relationship between risk factors, assesses the risk level, and uses social network analysis (SNA) to analyze the network of bridge construction accident risk factors. The results indicate that the more factors involved in risk coupling, the greater the safety risks in bridge construction. Human factors are susceptible to the influence of other elements, and environmental and management factors can directly or indirectly impact other factors. In addition, operational errors, a lack of supervision and management, inadequate safety inspections, poor management personnel, and insufficient technical capabilities are also key risk factors that need to be prevented and controlled.

Adaptive Local Information Transfer in Random Boolean Networks.

Living systems such as gene regulatory networks and neuronal networks have been supposed to work close to dynamical criticality, where their information-processing ability is optimal at the whole-system level. We investigate how this global information-processing optimality is related to the local information transfer at each individual-unit level. In particular, we introduce an internal adjustment process of the local information transfer and examine whether the former can emerge from the latter. We propose an adaptive random Boolean network model in which each unit rewires its incoming arcs from other units to balance stability of its information processing based on the measurement of the local information transfer pattern. First, we show numerically that random Boolean networks can self-organize toward near dynamical criticality in our model. Second, the proposed model is analyzed by a mean-field theory. We recognize that the rewiring rule has a bootstrapping feature. The stationary indegree distribution is calculated semi-analytically and is shown to be close to dynamical criticality in a broad range of model parameter values.

Hierarchical closeness efficiently predicts disease genes in a directed signaling network

BackgroundMany structural centrality measures were proposed to predict putative disease genes on biological networks. Closeness is one of the best-known structural centrality measures, and its effectiveness for disease gene prediction on undirected biological networks has been frequently reported. However, it is not clear whether closeness is effective for disease gene prediction on directed biological networks such as signaling networks. ResultsIn this paper, we first show that closeness does not significantly outperform other well-known centrality measures such as Degree, Betweenness, and PageRank for disease gene prediction on a human signaling network. In addition, we observed that prediction accuracy by the closeness measure was worse than that by a reachability measure, but closeness could efficiently predict disease genes among a set of genes with the same reachability value. Based on this observation, we devised a novel structural measure, hierarchical closeness, by combining reachability and closeness such that all genes are first ranked by the degree of reachability and then the tied genes are further ranked by closeness. We discovered that hierarchical closeness outperforms other structural centrality measures in disease gene prediction. We also found that the set of highly ranked genes in terms of hierarchical closeness is clearly different from that of hub genes with high connectivity. More interestingly, these findings were consistently reproduced in a random Boolean network model. Finally, we found that genes with relatively high hierarchical closeness are significantly likely to encode proteins in the extracellular matrix and receptor proteins in a human signaling network, supporting the fact that half of all modern medicinal drugs target receptor-encoding genes. ConclusionTaken together, hierarchical closeness proposed in this study is a novel structural measure to efficiently predict putative disease genes in a directed signaling network.

The relationship between modularity and robustness in signalling networks

Many biological networks tend to have a high modularity structural property and the dynamic characteristic of high robustness against perturbations. However, the relationship between modularity and robustness is not well understood. To investigate this relationship, we examined real signalling networks and conducted simulations using a random Boolean network model. As a result, we first observed that the network robustness is negatively correlated with the network modularity. In particular, this negative correlation becomes more apparent as the network density becomes sparser. Even more interesting is that, the negative relationship between the network robustness and the network modularity occurs mainly because nodes in the same module with the perturbed node tend to be more sensitive to the perturbation than those in other modules. This result implies that dynamically similar nodes tend to be located in the same module of a network. To support this, we show that a pair of genes associated with the same disease or a pair of functionally similar genes is likely to belong to the same module in a human signalling network.

A coherent feedforward loop design principle to sustain robustness of biological networks

Many studies have investigated the relationship between structural properties and dynamic behaviors in biological networks. In particular, feedback loop (FBL) and feedforward loop (FFL) structures have received a great deal of attention. One interesting and common property of FBL and FFL structures is their coherency of coupling. However, the role of coherent FFLs in relation to network robustness is not fully known, whereas that of coherent FBLs has been well established. To establish that coherent FFLs are abundant in biological networks, we examined gene regulatory and signaling networks and found that FFLs are ubiquitous, and are in a coherently coupled form. This result was also observed in the species-based signaling networks that are integrated from KEGG database. By using a random Boolean network model, we demonstrated that these coherent FFLs can improve network robustness against update-rule perturbations. In particular, we found that coherent FFLs increase robustness because these structures induce downstream nodes to be robust against update-rule perturbations. Therefore, coherent FFLs can be considered as a design principle of human signaling networks that improve network robustness against update-rule perturbations.

Robustness Analysis of a Boolean Model of Gene Regulatory Network with Memory

The response to different kinds of perturbations of a discrete model of gene regulatory network, which is a generalization of the random Boolean network (RBN) model, is discussed. The model includes memory effects, and the analysis pays particular attention to the influence on the system stability of a parameter (i.e., the decay time of the gene products) that determines the duration of the memory effects. It is shown that this parameter deeply affects the overall behavior of the system, with special regard to the dynamical regimes and the sensitivity. Furthermore, a noteworthy divergence in the response of systems characterized by different memory lengths in the presence of either temporary or permanent damages is highlighted, as is the substantial difference, with respect to classical RBNs, between the specific dynamical regime and the landscape of the attractors.

Intrinsic properties of Boolean dynamics in complex networks

We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffman's random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks ( 20 ⩽ N ⩽ 200 ). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of ℓ c in a network of size N consists of ℓ c states in the state space of 2 N states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps ℓ c states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffman's random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.

Attractor States of Boolean Dynamics in Complex Networks

One of the most remarkable features in “Life” or “Living Systems” is the coexistence between evolvability and robustness. Diversity of cell types in organisms is such a typical example. Indeed, Embryo-Stem (ES) cells differentiate into various types of cells with different phenotypes depending on the multiple environmental factors, and the cells can repeat the stable cell division. It is an irreversible transition in evolution as pointed out by Smith and Szathonany.1) The process of cell differentiation obeys a dynamical rule of the gene-gene interaction. Dynamics of Boolean networks has been studied as a simple model for variety of cell type in genetic networks since a pioneering work by Kauffman.2),3) A Boolean network consists of N nodes, each of which receives ki inputs such that the degree is ki. In the so-called Kauffman model — random Boolean network (RBN) model, each node receives a certain fixed number of inputs such that the degree is ki ≡ K. However, as a more realistic modeling of biological systems we expect that the fluctuation of the number of input-degree is treated as a random variable with a probability distribution function such as the inverse power-law distribution or the exponential distribution or the Poisson distribution. Actually it is demonstrated that the in-degree distribution appears to be exponential in E.coil and to be inverse power-law in yeast.4)–13) The relationship between the stability of network structure and the robustness of the attractors to the perturbation is very important for understanding the realistic gene regulatory networks (GRN) must be mutually correlated with each others. However, we deal with simple models in a sense that we simulate the Boolean dynamics in the fixed network structure and it does not influence the network growth. In the present paper, we investigate some intrinsic properties of attractor states in Boolean dynamics in complex networks with the fluctuation of the number of

Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data

In a previous study it was shown that a simple random Boolean network model, with two input connections per node, can describe with a good approximation (with the exception of the smallest avalanches) the distribution of perturbations in gene expression levels induced by the knock-out of single genes in Saccharomyces cerevisiae. Here we address the reason why such a simple model actually works: we present a theoretical study of the distribution of avalanches and show that, in the case of a Poissonian distribution of outgoing links, their distribution is determined by the value of the Derrida exponent. This explains why the simulations based on the simple model have been effective, in spite of the unrealistic hypothesis about the number of input connections per node. Moreover, we consider here the problem of the choice of an optimal threshold for binarizing continuous data, and we show that tuning its value provides an even better agreement between model and data, valuable also in the important case of the smallest avalanches. Finally, we also discuss the choice of an optimal value of the Derrida parameter in order to match the experimental distributions: our results indicate a value slightly below the critical value 1.

Dynamics of asynchronous random Boolean networks with asynchrony generated by stochastic processes

An asynchronous Boolean network with N nodes whose states at each time point are determined by certain parent nodes is considered. We make use of the models developed by Matache and Heidel [Matache, M.T., Heidel, J., 2005. Asynchronous random Boolean network model based on elementary cellular automata rule 126. Phys. Rev. E 71, 026232] for a constant number of parents, and Matache [Matache, M.T., 2006. Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126. IJMPB 20 (8), 897–923] for a varying number of parents. In both these papers the authors consider an asynchronous updating of all nodes, with asynchrony generated by various random distributions. We supplement those results by using various stochastic processes as generators for the number of nodes to be updated at each time point. In this paper we use the following stochastic processes: Poisson process, random walk, birth and death process, Brownian motion, and fractional Brownian motion. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed-point analysis. The dynamics of the system show that the number of nodes to be updated at each time point is of great importance, especially for the random walk, the birth and death, and the Brownian motion processes. Small or moderate values for the number of updated nodes generate order, while large values may generate chaos depending on the underlying parameters. The Poisson process generates order. With fractional Brownian motion, as the values of the Hurst parameter increase, the system exhibits order for a wider range of combinations of the underlying parameters.

ASYNCHRONOUS RANDOM BOOLEAN NETWORK MODEL WITH VARIABLE NUMBER OF PARENTS BASED ON ELEMENTARY CELLULAR AUTOMATA RULE 126

A Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which can vary from one node to another, is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in "Asynchronous Random Boolean Network Model Based on Elementary Cellular Automata Rule 126", Phys. Rev. E71, 026 232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be the same for all the nodes. We provide a model for the probability of finding a node in state 1 at a time t for the class of generalized asynchronous random Boolean networks (GARBN) in which a random number of nodes can be updated at each time point. We generate consecutive states of the network for both the real system and the models under the various schemes, and use simulation algorithms to show that the results match well. We use the model to study the dynamics of the system through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the GARBN's dynamics range from order to chaos, depending on the type of random variable generating the asynchrony and the parameter combinations.

Asynchronous random Boolean network model based on elementary cellular automata rule 126

This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary cellular automata. We provide formulas for the probability of finding a node in state 1 at a time t for the class of asynchronous random Boolean networks (ARBN) in which only one node is updated at every time step, and for the class of generalized ARBNs (GARBN) in which a random number of nodes can be updated at each time point. We use simulation methods to generate consecutive states of the network for both the real system and the models under the various schemes. The results match well. We study the dynamics of the models through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show, both theoretically and by example, that the ARBNs generate an ordered behavior regardless of the updating scheme used, whereas the GARBNs have behaviors that range from order to chaos depending on the type of random variable used to determine the number of nodes to be updated and the parameter combinations.

Modelling Vocabulary Loss

This paper describes some simple simulation models of vocabulary attrition. The attrition process is modelled using a random autonomous Boolean network model, and some parallels with real attrition data are drawn. The paper argues that applying a complex systems approach to attrition can provide some important insights, which suggest that real attrition data may need to be treated with caution. It concludes that simulation methods - a technique that is not widely used in applied linguistic research - may be able to throw interesting new light on attrition, and provide a way of examining some of the assumptions that we take for granted in attrition experiments with human subjects.

Random Boolean network model exhibiting deterministic chaos.

This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15, 17 (2001)]], who consider the same number of parents for all nodes. We make use of the same Boolean rule as Andrecut and Ali, provide a generalization of the formula for the probability of finding a node in state 1 at a time t, and use simulation methods to generate consecutive states of the network for both the real system and the model. The results match well. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the route to chaos is due to a cascade of period-doubling bifurcations which turn into reversed (period-halving) bifurcations for certain combinations of parameter values.

Modelling Bacterial Degradation of Organic Compounds with Genetic Networks

The bacterial degradation of organic compounds plays a crucial role in the biogeochemical cycles of the earth and in the clean-up of contaminated soils. The processes are carried out by bacterial consortia, rather than isolated strains, which are usually modelled by phenomenological kinetic equations which describe a fictitious, homogeneous bacterial species which mimics the behaviour of the consortium.An alternative modelling framework is presented here, where the bacterial consortia are considered as networks of genes interacting with other genes as well as with chemicals, which may be either introduced from outside or produced by bacterial metabolism. The model is based on an extension of the random Boolean network model of genetic networks, which makes use of continuous dynamical variables. Three different models are introduced, which differ in the way how they account for the existence of different species: (i) a single supercell model, where all the genes can interact strongly with each other; (ii) a graded interaction model, where genes interact strongly within a species, and weakly among different species; and (iii) a separate subsets model, where genes interact only within species. It is shown how this modelling framework is sound, as it is able to reproduce some of the generic behaviours of bacterial consortia, describing experimentally observed phenomena like population changes induced by contamination, and prey–predator dynamics.

Percolation thresholds in square-lattice Kauffman model

In Kauffman's random Boolean network model for genetics, each gene is either on or off, depending in a fixed random way on whether K neighbor genes are on or off. Our computer simulation puts these genes on the sites of a square lattice and asks if the "off" genes, the "on" genes, the "oscillating" genes and the non-oscillating "stable" genes are percolating, i.e. form one connected network of neighboring sites. The percolation thresholds for stable and for oscillating genes are found to coincide numerically with the transition to chaos at p = 0.29. Up to one million sweeps through the lattice were made to find that agreement.