Analysis and Control of Boolean Networks: A Semi-tensor - download pdf or read online

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 during which the weather behave in an on–off model. research and regulate of Boolean Networks offers a scientific new method of the research of Boolean regulate networks. the basic device during this method is a unique matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality might be expressed as a traditional discrete-time linear procedure. within the gentle of this linear expression, definite significant concerns relating Boolean community topology – mounted issues, cycles, temporary occasions and basins of attractors – might be simply published by way of a collection of formulae. This framework renders the state-space method of dynamic regulate structures acceptable to Boolean keep an eye on networks. The bilinear-systemic illustration of a Boolean keep watch over community makes it attainable to enquire simple keep an eye on difficulties together with controllability, observability, stabilization, disturbance decoupling, identity, optimum regulate, and so forth.

The ebook is self-contained, requiring simply wisdom of linear algebra and the fundamentals of the regulate concept of linear platforms. It starts with a brief advent to prepositional common sense and the techniques and homes of the STP and progressing through the (bi)linear expression of Boolean (control) networks to disturbance decoupling and decomposition of Boolean keep watch over structures. eventually multi-valued good judgment is taken into account as a extra specific manner 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 publication might be downloaded from http://lsc.amss.ac.cn/~dcheng/.

Analysis and keep watch over of Boolean Networks should be a basic reference for researchers in platforms biology, keep an eye on, structures technology and physics. The ebook used to be built for a brief path for graduate scholars and is acceptable for that objective. laptop scientists and logicians can also locate this publication to be of curiosity.

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

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Assume F ∈ L(U × V , R), that is, F is a bilinear mapping from U × V to R. Denote by {u1 , . . , um } and {v1 , . . , vn } the bases of U and V , respectively. We call S = (sij ) the structure matrix of F , where sij = F (ui , vj ), i = 1, . . , m, j = 1, . . , n. T If we let X = m i=1 xi ui ∈ U , otherwise written as X = (x1 , . . , xm ) ∈ U , and n T Y = i=1 yi vi ∈ V , otherwise written as Y = (y1 , . . , yn ) ∈ V , then F (X, Y ) = X T SY. 14) Denoting the rows of S by S 1 , . . , S m , we can alternatively calculate F in two steps.

Then ZW[m,t] A = AZW[n,t] = A ⊗ Z. 70) 2. Let Y be a t-dimensional column vector and A ∈ Mm×n . Then AW[t,n] Y = W[t,m] Y A = A ⊗ Y. 4 Properties of the Semi-tensor Product 45 The following lemma is useful for simplifying some expressions. 1 Let A ∈ Mm×n . Then W[m,q] W[q,n] = Iq ⊗ A. 72) The semi-tensor product has some pseudo-commutative properties. The following are some useful pseudo-commutative properties. Their usefulness will become apparent later. 18 Suppose we are given a matrix A ∈ Mm×n .

Arrange it into a matrix by using the ordered multi-index Id(i1 , i2 , . . , is ; n) for columns and the ordered multi-index Id(j1 , j2 , . . , jt ; n) for rows. 27) Mφ = ⎢ . ⎥. ⎢ . ⎥ ⎣ . ⎦ 11···1 · · · c11···n · · · cnn···n cnn···n nn···n nn···n It is the structure matrix of the tensor φ. Now, assume ωi ∈ V ∗ , i = 1, 2, . . , t, and Xj ∈ V , j = 1, 2, . . , s, where ωi are expressed as rows, and Xj are expressed as columns. Then φ(ω1 , . . , ωt , X1 , . . 28) is omitted. Next, we define the power of a matrix.

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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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