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Analysis and Control of Boolean Networks: A Semi-tensor Product Approach

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Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc.

Motivated by the Human Genome Project, a new view of biology, called systems biology, is emerging [5]. Systems biology does not investigate individual genes, proteins or cells in isolation. Rather, it studies the behavior and relationships of all of the cells, proteins, DNA and RNA in a biological system called a cellular network. The most active networks may be those associated with genetic regulation, which regulate the growth, replication, and death of cells in response to changes in the environment.

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