Attractor-Based Simultaneous Design of the Minimum Set of Control Nodes and Controllers in Boolean Networks

Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a controller is studied. A control node corresponds to a gene that expression can be controlled. Here, a Boolean network is used as a model of gene regulatory networks, and control specifications on attractors, which represent cell types or states of cells, are imposed. It is important to design a gene regulatory network that has desired attractors and has no undesired attractors. Using a matrix-based representation of BNs, this problem can be rewritten as an integer linear programming problem. Finally, the proposed method is demonstrated by a numerical example on a WNT5A network, which is related to melanoma.

Input Structure Design for Structural Controllability of Complex Networks

This paper addresses the problem of the input design of large-scale complex networks.Two types of network components,redundant inaccessible strongly connected component(RISCC)and intermittent inaccessible strongly connected component(IISCC)are defined,and a subnetwork called a driver network is developed.Based on these,an efficient method is proposed to find the minimum number of controlled nodes to achieve structural complete controllability of a network,in the case that each input can act on multiple state nodes.The range of the number of input nodes to achieve minimal control,and the configuration method(the connection between the input nodes and the controlled nodes)are presented.All possible input solutions can be obtained by this method.Moreover,we give an example and some experiments on real-world networks to illustrate the effectiveness of the method.

Research on the Controllability of Software Networks Based on the Source-Driven Model

The complexity of software system has been increasing with software evolution, which affects the stability of software structure. Most of the existing measurement methods focus on the analysis of the macro-characteristics of the network topology, but lacked a certain depth and expansion to explore the nature of the complexity of the software structure, for this purpose, the complex network control theory was applied to the study of software network controllability. Firstly, the Source-Driver (SD) model was established based on the system control theory, the driver node sets were obtained by the minimum input theorem in the control process of software network topology;Then the relationship between the degree and center degree, the relationship between the in-degree and the out-degree of the software network topology were further analyzed owing to the non-uniqueness of the driver node sets;Finally, the values of the four indicators in the software system were compared. Experimental results show that the driver node sets in the software networks are mainly composed of nodes with low degree values, but it does not mean that the nodes whose in-degree values and out-degree values are also low;The action on control nodes and driver nodes are not random, the controllability of the driver nodes is closely related to the in-degree, when selecting the driver node sets, the network topology characteristics should be considered comprehensively, and the nodes with high degree and center degree are the first choice. The results have important guiding significance for the control, maintenance and redesign of software architecture.

Lagrange Interpolation on a Sphere

In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.

Finding Key Node Sets in Complex Networks Based on Improved Discrete Fireworks Algorithm

Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is defined firstly.Because it is an NP-hard combinatorial optimization problem,discrete fireworks algorithm is introduced to search the optimal solution,which is a swarm intelligence algorithm and is improved by the prior information of networks.To verify the effect of improved discrete fireworks algorithm(IDFA),experiments are carried out on various model networks and real power grid.Results show that the proposed IDFA is obviously superior to the benchmark algorithms,and networks suffer more damage when the key node sets obtained by IDFA are removed from the networks.The key node sets found by IDFA contain a large number of non-central nodes,which provides the authors a new perspective that the seemingly insignificant nodes may also have an important impact on the robustness of the network.