Download Analysis and Control of Boolean Networks: A Semi-tensor by Daizhan Cheng, Hongsheng Qi, Zhiqiang Li PDF

By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

The Boolean community has turn into a strong instrument for describing and simulating mobile networks during which the weather behave in an on–off type. research and keep an eye on of Boolean Networks offers a scientific new method of the research of Boolean keep watch over networks. the elemental device during this method is a singular matrix product known as the semi-tensor product (STP). utilizing the STP, a logical functionality could be expressed as a traditional discrete-time linear procedure. within the mild of this linear expression, convinced significant concerns bearing on Boolean community topology – fastened issues, cycles, temporary instances and basins of attractors – should be simply published by way of a collection of formulae. This framework renders the state-space method of dynamic regulate structures acceptable to Boolean regulate networks. The bilinear-systemic illustration of a Boolean keep an eye on community makes it attainable to enquire simple regulate difficulties together with controllability, observability, stabilization, disturbance decoupling, id, optimum regulate, and so forth.

The booklet is self-contained, requiring merely wisdom of linear algebra and the fundamentals of the keep watch over idea of linear structures. It starts with a brief advent to prepositional common sense and the innovations and houses of the STP and progressing through the (bi)linear expression of Boolean (control) networks to disturbance decoupling and decomposition of Boolean keep an eye on platforms. eventually multi-valued good judgment is taken into account as a extra unique approach of describing actual networks and stochastic Boolean networks are touched upon. appropriate numerical calculations are defined in an appendix and a MATLAB® toolbox for the algorithms within the booklet may be downloaded from

Analysis and keep an eye on of Boolean Networks might be a primary reference for researchers in structures biology, regulate, structures technology and physics. The e-book used to be built for a quick direction for graduate scholars and is acceptable for that goal. laptop scientists and logicians can also locate this booklet to be of curiosity.

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

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This yields multivalued logic. If we allow the values to be anything between 1 and 0, we have fuzzy logical values. Next, we define multivalued logic and fuzzy logic rigorously. ,F = 0 Dk = T = 1, k−1 k−1 and Df = {r | 0 ≤ r ≤ 1}. Note that D2 = D is what we defined before for Boolean logic. 7 1. A logical system is called a k-valued logic if its logical variables may take any values from Dk . 2. A logical system is called a fuzzy logic if its logical variables may take any values from Df . 11 k-valued unary operators ¬p p k (p) i,k (p) 1 0 (k − 2)/(k − 1) 0 (k − 2)/(k − 1) ..

8. If A and B are invertible, then A B ∼ B A. 9. If A and B are invertible, then (A B)−1 = B −1 A−1 . 101) 10. If A ≺t B, then If A t t det(A B) = det(A) det(B). det(A B) = det(A) det(B) .

Eis , ej1 , ej2 , . . ,jt 1 ≤ i1 , . . , is , j1 , . . , jt ≤ n is the set of structure constants of φ. Structure constants of φ ∈ Tt s form a set of (s + t)-dimensional data. Next, we consider how to arrange higher-dimensional data. In linear algebra onedimensional data are arranged as a column or a row, called a vector, while twodimensional data are arranged as a rectangle, called a matrix. In these forms matrix computation becomes a very convenient and powerful tool for dealing with oneor two-dimensional data.

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