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Using semi-tensor product, the Boolean network is converted into its algebraic form as a standard discrete-time linear system. From the rank and 1-eigenvector of structure matrix, we obtain the cycle structure of the Boolean network, such as the cycles and the number of the cycles with different length. In this paper, we just use the rank and 1-eigenvector of structure matrix to obtain the results, while in literature the different powers of structure matrix are used. [ABSTRACT FROM PUBLISHER]

The potentiality of using a common developmental mapping to develop not a specific, but different classes of architectures (i.e., species), holding different structural and/or computational phenotypic properties is an active area of research in the field of bio-inspired systems. To be able to develop such species, there is a need to understand the governing properties and the constraints involved for their development. In this work we investigate the ability of common developmental genomes to evolve more than one specie (i.e., computational architecture), towards problems with increasing complexity. The architectures considered as different species were cellular automata and boolean networks and the problem studied was a simple financial market model over various architecture sizes. We considered problem instances of the same problem, each having a higher level of complexity, i.e., an instance with no state memory and with a previous memory of 1-, 2-, 5- and 10-state. The results show that the common developmental genome was able to find better results for certain cell architectures sizes. [ABSTRACT FROM PUBLISHER]

One of the ultimate objectives of studying gene regulatory networks is to derive potential intervention strategies to avoid aberrant cellular behavior. Boolean networks (BNs) and their stochastic extension, probabilistic Boolean networks (PBNs), provide a convenient framework to design different types of intervention strategies. In this paper, we focus on studying structural intervention, in which we perturb regulatory Boolean functions to alter the long-term network dynamics to obtain desirable behavior. Specifically, we extend our previous work that derives optimal structural intervention for rank-1 function perturbations to more general solutions for arbitrary rank-k function perturbations. The analytic solution is derived using the Sherman-Morrison-Woodbury (SMW) formula. We apply the derived structural intervention to a mutated mammalian cell cycle network. Our results show that our intervention strategy correctly identifies the main targets to stop uncontrolled cell growth in the mutated cell cycle network. [ABSTRACT FROM PUBLISHER]

ABSTRACT In this paper, a new stationary control policy in Boolean networks (BNs) is derived based on the structural properties of basins of attraction (BOA). The new greedy control policy guarantees that no new attractor cycles will be created by intervention to the original BNs. Hence, it will not introduce significant steady-state mass to ambiguous network states, which may represent unknown phenotypes corresponding to potential collateral damage. Comparing the control performance of this new phenotypically constrained BOA control policy with previous control policies based on long-run network behavior, the experiments based on randomly generated networks have shown that the new control policy obtains competitive performance with reduced complexity. [ABSTRACT FROM PUBLISHER]

The problem of approximation to large-scale Boolean networks is considered. First, we assume a large-scale Boolean network is aggregated into several sub-networks. Using the outputs(or inputs) of each sub-network as new state variables, a new simplified time-varying network is obtained. Then a time-invariant Boolean network is used to approximate each subsystem. Observed data are used to find the best approximating dynamic models. Finally, the aggregation method is investigated. [ABSTRACT FROM PUBLISHER]

Control of finite-valued networks, including Boolean networks, is currently a hot topic. In this paper the optimization control of the networks with present value performance criterion is discussed. The problem is formulated as a finite strategy game between human and machine. It is firstly proved that the optimal strategy can be found in the set of periodic strategies, which makes the problem finitely computable, though the computational complexity of exhaustion might be a severe problem. Then an efficient numerical method is developed to solve the problem. Some interesting examples are presented to demonstrate the efficiency of our results. [ABSTRACT FROM PUBLISHER]

This paper investigates how to define and construct a Lyapunov function for Boolean networks, and presents a number of new results based on the semi-tensor product of matrices. A proper form of pseudo-Boolean functions is found, and the concept of (strict-)Lyapunov functions is thus given. It is shown that a pseudo-Boolean function in the proper form can play the role of Lyapunov functions for Boolean networks, based on which some Lyapunov-based stability results are obtained. Then, we study how to construct a Lyapunov function for Boolean networks, and propose a definition-based method. The study of illustrative examples shows that the new results/method presented in this paper work very well. [ABSTRACT FROM PUBLISHER]

This paper investigates the function perturbation impact on the topological structure of Boolean networks by using the semi-tensor product method, and presents a set of new results. First, a new necessary and sufficient condition is presented to guarantee that an attractor is invariant after function perturbations. Second, a necessary and sufficient condition is established to analyze how do the attractors of Boolean networks change with the Boolean function perturbations. Finally, as applications, the intervention problem of a WNT5A Boolean network and the function perturbation identification problem of a D. melanogaster segmentation polarity gene network are investigated, respectively. The study of the practical examples shows that the new results obtained in this paper are very effective in the function perturbations impact analysis of Boolean networks. [ABSTRACT FROM PUBLISHER]

The stability of biological organisms is a major feature which contributes to their survival in the environment. However, the study of the stability in vivo is a very hard challenge. An objective way for the stability analysis is to adopt the Boolean network model, which can qualitatively describe the behavior of biological networks as well as allows the analysis of the results in a comprehensive and global way. Besides, certain Boolean function classes play an important role in Boolean network stability. In addition to this relationship, it is expected that many classes of network topology assigns greater or lesser resistance to damage. In this work, we define “local stability” as the stability resulted from the presence of a certain Boolean function class, such as the canalyzing Boolean functions, and “global stability” as the result of a certain network topology, such as the scale-free topology. Next, we investigate the interaction between these two factors using the size of the largest basin of attraction and generalized Derrida curves as measures for network stability. Our results show that there is a “topology order” for certain Boolean function classes, and that these two factors should be jointly addressed in future analysis of network stability. [ABSTRACT FROM PUBLISHER]

Numerous approaches exist for modeling of genetic regulatory networks (GRNs) but the low sampling rates often employed in biological studies prevents the inference of detailed models from experimental data. In this paper, we analyze the issues involved in estimating a model of a GRN from single cell line time series data with limited time points. We present an inference approach for a Boolean Network (BN) model of a GRN from limited transcriptomic or proteomic time series data based on prior biological knowledge of connectivity, constraints on attractor structure and robust design. Through theoretical analysis and simulations, we showed the rarity of arriving at a BN from limited time series data with plausible biological structure using random connectivity and absence of structure in data. We applied our inference approach to 6 time point transcriptomic data on HMEC cell lines after application of EGF and generated a BN with a plausible biological structure satisfying the data. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a definition for the essentiality of regulatory relationships among molecules in a Boolean network model, which takes the regulatory relationships between the molecules into account, in addition to their connectivity. The proposed definition of essentiality is tightly related to the ultimate goal of designing intervention strategies to achieve beneficial dynamic changes in the network. Focusing on Boolean networks, we define the essentiality of each regulatory relationship as the difference between the expected performance of the Bayesian robust structural intervention over the uncertainty class of networks, which arises from the uncertainty in the given regulatory relationship, and the performance of the optimal structural intervention for the known network in which there is no uncertainty. For a specific regulatory relationship, a large difference in performance implies that the given relationship is critical for designing effective therapeutic strategies. On the other hand, small difference implies that the regulatory relationship under consideration may not be crucial in designing intervention strategies. This new definition of essentiality, grounded on the quantification of uncertainty in network dynamics, may provide a deep understanding of the robustness, adaptability, and controllability of gene regulatory networks. [ABSTRACT FROM PUBLISHER]