Abstract Boolean Network Research Articles

Autonomous Boolean network regulation based on logic gates’ response characteristics

Boolean networks (BNs) are nonlinear systems and each BN has a simple structure, thus it is easy to construct large networks. The BNs are becoming increasingly important as they have been widely used in many fields like random number generation, gene regulation, and reservoir computing. In recent years, autonomous Boolean networks (ABNs) have been proposed and realized by actual digital logic circuit. The BNs each have a clock or selection device to determine the update time of each node. Unlike BNs, ABNs have no device to control the update mechanism, and the update of each node is determined by response characteristics of the logic gate that make up the node, which leads to continuous and complicated outputs. Time series with different complexities including periodic and chaotic sequences can be generated by the ABNs, which is very meaningful in different applications.Research on the regulation of ABNs’ output is of big significance. Non-ideal response characteristics of the logic gates and time delay on the link are two major factors which can regulate the output state. Many studies focus on time delay on the link and indicate that the large delay inconsistency leads to complex outputs.In this paper, in order to study the regulation of ABNs’ output, it is demonstrated that the response characteristics of the logic gate can be continuously adjusted by the parameters in the ABNs’ equations. Then the effects of logic gates’ response characteristics on ABNs’ outputs are studied by simulation. The simulation results indicate that the ABNs’ outputs can transform between periodic and chaotic state with the change of logic gates’ response characteristics. Moreover, the interrelationship between logic gates’ response characteristics and propagation delays along the links is reinvestigated. The results show that the high complexity series space is extended by the fast logic gates’ response characteristics. Also the effects of different logic gates’ response characteristics on the ABNs’ output are compared, and the results indicate that node 2 has a good performance on the regulation of ABNs’ output while node 1 and node 3 show small effect on the ABNs’ output.It is concluded that the complexity of the ABNs’ output can be regulated by the logic gates’ response characteristics, and the high complexity series’ generation can be promoted by the fast logic gates’ response characteristics. This conclusion is conducive to the logic gates’ selection in random number generation, gene regulation, reservoir computing and other applications.

On the Lyapunov Exponent of Monotone Boolean Networks †

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.

Lightweight Boolean Network Tomography Based on Partition of Managed Networks

Boolean network tomography is a promising technique to achieve fault management in networks where the existing IP-based troubleshooting mechanism cannot be used. Aiming to apply Boolean network tomography to fault management, a variety of heuristic methods for configuring monitoring trails and paths have been proposed to localize link failures in managed networks. However, these existing heuristic methods must be executed in a centralized server that administers the entire managed network and the methods present scalability problems when applied to large-scale managed networks. Thus, this paper proposes a novel scheme for achieving lightweight Boolean network tomography in a decentralized manner. The proposed scheme partitions the managed network into multiple management areas and localizes link failures independently within each area. This paper also proposes a heuristic network partition method with the aim of efficiently implementing the proposed scheme. The effectiveness of the proposed scheme is verified using typical fault management scenarios where all single-link failures and all dual-link failures are localized by the least number of monitoring paths on predetermined routes. Simulation results show that the proposed scheme can greatly reduce the computational load on the fault management server when Boolean network tomography is deployed in large-scale managed networks. Furthermore, the degradation of optimality in the proposed scheme can be mitigated in comparison with a centralized scheme that utilizes heuristics to reduce the computational load on the centralized server.

An Efficient Steady-State Analysis Method for Large Boolean Networks with High Maximum Node Connectivity.

Boolean networks have been widely used to model biological processes lacking detailed kinetic information. Despite their simplicity, Boolean network dynamics can still capture some important features of biological systems such as stable cell phenotypes represented by steady states. For small models, steady states can be determined through exhaustive enumeration of all state transitions. As the number of nodes increases, however, the state space grows exponentially thus making it difficult to find steady states. Over the last several decades, many studies have addressed how to handle such a state space explosion. Recently, increasing attention has been paid to a satisfiability solving algorithm due to its potential scalability to handle large networks. Meanwhile, there still lies a problem in the case of large models with high maximum node connectivity where the satisfiability solving algorithm is known to be computationally intractable. To address the problem, this paper presents a new partitioning-based method that breaks down a given network into smaller subnetworks. Steady states of each subnetworks are identified by independently applying the satisfiability solving algorithm. Then, they are combined to construct the steady states of the overall network. To efficiently apply the satisfiability solving algorithm to each subnetwork, it is crucial to find the best partition of the network. In this paper, we propose a method that divides each subnetwork to be smallest in size and lowest in maximum node connectivity. This minimizes the total cost of finding all steady states in entire subnetworks. The proposed algorithm is compared with others for steady states identification through a number of simulations on both published small models and randomly generated large models with differing maximum node connectivities. The simulation results show that our method can scale up to several hundreds of nodes even for Boolean networks with high maximum node connectivity. The algorithm is implemented and available at http://cps.kaist.ac.kr/∼ckhong/tools/download/PAD.tar.gz.

Synchronization Analysis of Boolean Network

Boolean network and its synchronization have been gradually used to the global behavior analysis of large gene regulatory network. Network synchronization depends mainly on the dynamics of each node and the topology of the network. In this paper, using the semi-tensor product of matrices, a necessary and sufficient condition based on transition matrix for Boolean network complete synchronization is presented. The synchronization of Boolean control network is also discussed. Two examples are given to illustrate the theoretical result.