P_UNSAT approach of attractor calculation for Boolean gene regulatory networks.

Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which combined the predecessor approach and the logic unsatisfiability approach to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks even the networks with a relatively large average degree.

An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks.

Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which improved the predecessor-based approach. Furthermore, the proposed approach combined with the identification of constant nodes and simplified Boolean networks to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks. If the average degree of the network is not too large, the algorithm can get all attractors of a Boolean network with dozens or even hundreds of nodes.

Investigation of oscillation accumulation triggered genetic switch in gene regulatory networks.

Genetic oscillator motifs and genetic switch motifs are blocks of biochemical reaction networks, which are involved in the regulation of rhythms, cell cycle progression, signal processing and cell fate decision. These motifs often interact to constitute complex signal processing systems. There widely exists the oscillation accumulation triggered mechanism in gene regulatory networks, i.e., an oscillator promotes the accumulation of a signaling protein over a threshold value, and activates a switch. The structure can be fund in some important biological function switches, such as apoptosis and DNA repair. We propose the structure as an oscillation accumulation triggered genetic switch (OATGS). Through mathematical modeling and analysis, results show the OATGS with features of robustness to noise and triggered mode. In addition, we show the existence of OATGS features and triggered manner in p53 gene regulatory networks, and explain some of the p53 regulation process, such as counting mechanism and pulse shape. We speculate that OATGS with oscillation accumulation triggered manner is a new important biological function switch.

The interaction between multiplex community networks.

Multiplex community networks, consisting of several different types of simplex networks and interconnected among them, are ubiquitous in the real world. In this paper, we carry out a quantitative discussion on the interaction among these diverse simplex networks. First, we define two measures, mutual-path-strength and proximity-node-density, based on twoplex community networks and then propose an impact-strength-index (ISI) to describe the influence of a simplex network on the other one. Finally, we apply the measure ISI to make an explanation for the challenge system of social relations from the viewpoint of network theory. Numerical simulations show that the measure ISI can describe the interaction between multiplex community networks perfectly.

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations.

Universal perceptron (UP), a generalization of Rosenblatt's perceptron, is considered in this paper, which is capable of implementing all Boolean functions (BFs). In the classification of BFs, there are: 1) linearly separable Boolean function (LSBF) class, 2) parity Boolean function (PBF) class, and 3) non-LSBF and non-PBF class. To implement these functions, UP takes different kinds of simple topological structures in which each contains at most one hidden layer along with the smallest possible number of hidden neurons. Inspired by the concept of DNA sequences in biological systems, a novel learning algorithm named DNA-like learning is developed, which is able to quickly train a network with any prescribed BF. The focus is on performing LSBF and PBF by a single-layer perceptron (SLP) with the new algorithm. Two criteria for LSBF and PBF are proposed, respectively, and a new measure for a BF, named nonlinearly separable degree (NLSD), is introduced. In the sense of this measure, the PBF is the most complex one. The new algorithm has many advantages including, in particular, fast running speed, good robustness, and no need of considering the convergence property. For example, the number of iterations and computations in implementing the basic 2-bit logic operations such as AND, OR, and XOR by using the new algorithm is far smaller than the ones needed by using other existing algorithms such as error-correction (EC) and backpropagation (BP) algorithms. Moreover, the synaptic weights and threshold values derived from UP can be directly used in designing of the template of cellular neural networks (CNNs), which has been considered as a new spatial-temporal sensory computing paradigm.

Universal perceptron and DNA-like learning algorithm for binary neural networks: non-LSBF implementation.

Implementing linearly nonseparable Boolean functions (non-LSBF) has been an important and yet challenging task due to the extremely high complexity of this kind of functions and the exponentially increasing percentage of the number of non-LSBF in the entire set of Boolean functions as the number of input variables increases. In this paper, an algorithm named DNA-like learning and decomposing algorithm (DNA-like LDA) is proposed, which is capable of effectively implementing non-LSBF. The novel algorithm first trains the DNA-like offset sequence and decomposes non-LSBF into logic XOR operations of a sequence of LSBF, and then determines the weight-threshold values of the multilayer perceptron (MLP) that perform both the decompositions of LSBF and the function mapping the hidden neurons to the output neuron. The algorithm is validated by two typical examples about the problem of approximating the circular region and the well-known n-bit parity Boolean function (PBF).