| Boolean network is an important model for the study of gene regulatory networks.It can simulate the dynamic behavior of genes interaction.As a result,the research on the dynamic characteristics of Boolean networks has attracted much attention in China and abroad.In recent years,Boolean network has played an important role in exploring the mechanism of life activity,researching the cause of disease and developing treatment methods.For an example,constructing a genetic regulatory network to understand the interaction between genes can help understand the genetic regulatory mechanisms of specific tissues,which in turn could be helpful in developing disease treatment methods.Nevertheless,current the theoretical analysis of Boolean network model is still relatively weak due to the lack of mathematical tools to study logic system.In recent years,Cheng and its team have proposed a matrix semi-tensor product,which provides a new theoretical tool for the study of Boolean networks.The method of semi-tensor product transforms the Boolean network dynamic system into a discrete algebraic dynamic system,which provides a generalized theoretical framework for the study of Boolean networks.This paper studies the optimal energy control of Boolean Network.Firstly,related concepts of Boolean dynamic networks are introduced;Secondly using the mathematical tool of matrix semi-tensor product,the logical operation is transformed into matrix operation by establishing the correspondence relation between logical variables and vectors.The logic dynamic control system is then transformed into an ordinary discrete dynamic system.Base on the semi-tensor expression of the index of logic vector established,the function of energy consumption of Boolean network is turn into a semi-tensor product form,the dynamic programming theorem and maximum principle are constructed.These provided new methods for studying the optimal energy consumption of Boolean network.Finally,the method is verified using examples. |
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