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

By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

ISBN-10: 0857290967

ISBN-13: 9780857290960

ISBN-10: 0857290975

ISBN-13: 9780857290977

The Boolean community has develop into a robust device for describing and simulating mobile networks within which the weather behave in an on–off type. research and regulate of Boolean Networks provides a scientific new method of the research of Boolean keep an eye on networks. the elemental device during this procedure is a singular matrix product known as the semi-tensor product (STP). utilizing the STP, a logical functionality could be expressed as a standard discrete-time linear method. within the gentle of this linear expression, definite significant matters relating Boolean community topology – fastened issues, cycles, brief instances and basins of attractors – may be simply printed via a suite of formulae. This framework renders the state-space method of dynamic regulate structures acceptable to Boolean keep watch over networks. The bilinear-systemic illustration of a Boolean keep an eye on community makes it attainable to enquire uncomplicated keep watch over difficulties together with controllability, observability, stabilization, disturbance decoupling, id, optimum keep watch over, and so on.

The e-book is self-contained, requiring purely wisdom of linear algebra and the fundamentals of the keep watch over thought of linear structures. It starts off with a quick creation to prepositional common sense and the suggestions and homes of the STP and progressing through the (bi)linear expression of Boolean (control) networks to disturbance decoupling and decomposition of Boolean regulate structures. ultimately multi-valued common sense is taken into account as a extra unique approach of describing genuine networks and stochastic Boolean networks are touched upon. proper numerical calculations are defined in an appendix and a MATLAB® toolbox for the algorithms within the e-book will be downloaded from http://lsc.amss.ac.cn/~dcheng/.

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

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

Sample text

2 1. In R3 we define a three linear mapping as φ(X, Y, Z) = X × Y, Z , X, Y, Z ∈ R3 , where ·, · denotes the inner product. Its geometric interpretation is the volume of the parallelogram with X, Y , Z as three adjacent edges [when (X, Y, Z) form a right-hand system, the volume is positive, otherwise, the volume is negative]. It is obvious that φ is a tensor with covariant degree 3. 2. In R3 we can define a four linear mapping as ψ(X, Y, Z, W ) = X × Y, Z × W , X, Y, Z, W ∈ R3 . Obviously, ψ is a tensor of covariant degree 4.

Unlike the conventional matrix product, for the semi-tensor product even A B and B C are well defined, but A B C = (A B) C may not be well defined. For instance, A ∈ M3×4 , B ∈ M2×3 , C ∈ M9×1 . In the conventional matrix product the equal dimension condition has certain physical interpretation. For instance, inner product, linear mapping, or differential of compound multiple variable function, etc. , the product of different-dimensional data, tensor product, etc. We give one more example. , Δk = Col{Ik } = δki i = 1, 2, .

2. Let T T T T T B = B11 , . . , B1n , . . , Bm1 , . . , Bmn , where each block has the same dimension and the blocks are labeled by double index {i, j } and arranged by the ordered multi-index Id(i, j ; m, n). Then T T T T W[m,n] B = B11 , . . , Bm1 , . . , B1n , . . , Mmn T consists of the same set of blocks, which are arranged by the ordered multi-index Id(j, i; n, m). The product of a matrix with an identity matrix I has some special properties. 13 1. Let M ∈ Mm×pn . Then In = M. 60) Ipn = M ⊗ Ip .

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


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