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The interactions among different genes, proteins and other small molecules are becoming more and more significant and have been studied intensively nowadays. One general way that helps people understand these interactions is to analyze networks constructed from genes/proteins. In particular, module structure as a common property of most biological networks has drawn much attention of researchers from different fields. In most cases, biological networks can be corrupted by noise in the data and the corruption may cause mis-identification of module structure. Besides, some structure may be destroyed when improper experimental settings are built up. Thus module structure may be unstable when one single network is employed. In this paper, we consider employing multiple networks for consistent module detection in order to reduce the effect of noise and experimental setting. Instead of considering different networks separately, our idea is to combine multiple networks together by building them into tensor structure data. Then given any node as prior label information, tensor-based Markov chains are constructed iteratively for identification of the modules shared by the multiple networks. In addition, the proposed tensor-based Markov chain algorithm is capable of simultaneously evaluating the contribution from each network. It would be useful to measure the consistency of modules in the multiple networks. In the experiments, we test our method on two groups of gene co-expression networks from human beings. We also validate the modules identified by the proposed method.

Network module (community) structure has been a hot research topic in recent years. Many methods have been proposed for module detection and identification. Hierarchical structure of modules is shown to exist in different kinds of biological networks. Compared to the module identification methods, less research is done on the hierarchial structure of modules. In this paper, we propose a method for constructing the hierarchical modular structure in networks based on the extended random graph model. Statistical tests are applied to test the hierarchial relations between different modules. We give both artificial networks and real data examples to illustrate the performance of our approach. Application of the proposed method to yeast gene co-expression network shows that it does have a hierarchical modular structure with the modules on different levels corresponding to different gene functions.

Efficient coverage area and efficient coverage area ratio of node are put forward by analysis of coverage problem of wireless sensor networks (WSN). It is theoretically proved through math modeling, theoretical analysis and formula deducting that how much the maximum efficient coverage area, the maximum efficient coverage area ratio, the maximum of net efficient coverage area and the maximum of net efficient coverage area ratio of node is if full seamless coverage is met in wireless sensor networks. At last, the analysis formula is given that minimum number of radio nodes is demanded in a given sensor field if the field is covered fully and seamlessly. The formula resolves a math problem of wireless sensor networks in theory. The research on the size of nodes has significant meanings of theory research and networks designing of wireless sensor networks.

The construction of genetic regulatory networks from time series gene expression data is an important research topic in bioinformatics as large amounts of quantitative gene expression data can be routinely generated nowadays. One of the main difficulties in building such genetic networks is that the data set has huge number of genes but small number of time points. In this paper, we propose a linear regression model for uncovering the relations among the genes by using multiple regression method with filtering. The model takes into account of the fact that real biological networks have the scale-free property. Based on this property and the statistical tests, a filter can be constructed and the interactions among the genes can be inferred by minimizing the distance between the observed data and the predicted data. Numerical examples based on yeast gene expression data are given to demonstrate our method.

The construction and control of genetic regulatory networks using gene expression data is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the number of genes is large because of the huge computational cost. In this paper, we propose a simplified multivariate Markov model for approximating a PBN. The new model can preserve the strength of PBNs and at the same time reduce the complexity of the network and therefore the computational cost. We then present an optimal control model with hard constraints for the purpose of control/intervention of a genetic regulatory network. Numerical experimental examples based on the yeast data are then given to demonstrate the effectiveness of our proposed model and control policy.

This paper considers the problem of finding global states incoming to a specified global state in a Boolean network, which may be useful for pre-processing of finding a sequence of control actions for a Boolean network and for identifying the basin of attraction for a given attractor. We show that this problem is NP-hard in general along with related theoretical results. On the other hand, we present algorithms that are much faster than the naive exhaustive search-based algorithm.

In this paper, we propose a linear control model for gene intervention in a genetic regulatory network. At each time step, finite controls are allowed to drive the network states to some target states. The objective is to achieve a target state probability distribution with a minimal control cost. The model can be formulated as a minimization problem with integer variables and continuous variables. Our experimental results show that the control model and the algorithm are efficient for gene intervention problems in genetic networks.