By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

ISBN-10: 0857290967

ISBN-13: 9780857290960

ISBN-10: 0857290975

ISBN-13: 9780857290977

The Boolean community has turn into a strong instrument for describing and simulating mobile networks within which the weather behave in an on–off style. research and regulate of Boolean Networks provides a scientific new method of the research of Boolean keep watch over networks. the elemental instrument during this technique is a unique matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality will be expressed as a standard discrete-time linear method. within the mild of this linear expression, yes significant concerns bearing on Boolean community topology – mounted issues, cycles, brief instances and basins of attractors – might be simply published via 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 regulate community makes it attainable to enquire simple keep an eye on difficulties together with controllability, observability, stabilization, disturbance decoupling, identity, optimum regulate, and so on.

The booklet is self-contained, requiring purely wisdom of linear algebra and the fundamentals of the keep watch over idea of linear structures. It starts with a quick creation to prepositional common sense and the thoughts 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 common sense is taken into account as a extra specified means of describing actual 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 ebook should 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 platforms biology, keep an eye on, structures technological know-how and physics. The e-book was once constructed for a brief direction for graduate scholars and is appropriate for that function. 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**

For instance, if prisoner P1 chooses “mum” (A1 ) and P2 chooses “fink” (A2 ), P1 will be sentenced to jail for nine months and P2 will be released. Now, if we denote by i rj,k , i = 1, 2, j = 1, 2, k = 1, 2, i } is a set the payoff of Pi as P1 takes strategy j and P2 takes strategy k, then {rj,k of 3-dimensional data. We may arrange it into a payoff matrix as Mp = 1 r11 1 r12 1 r21 1 r22 2 r11 2 r12 2 r21 2 r22 = −1 −9 −1 0 0 −6 −9 −6 . 2 Semi-tensor Product of Matrices 29 2. Consider a game with n players.

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. Step 1: Calculate x1 S 1 , x2 S 2 , . . , xm S m and take their sum.

Let M ∈ Mm×n . Then M 3. Let M ∈ Mpm×n . Then Ip 44 2 Semi-tensor Product of Matrices M = M ⊗ Ip . 63) 4. Let M ∈ Mm×n . Then Ipm In the following, some linear mappings of matrices are expressed in their stacking form via the semi-tensor product. 14 Let A ∈ Mm×n , X ∈ Mn×q , Y ∈ Mp×m . Then Vr (AX) = A Vr (X), Vc (Y A) = A T Vc (Y ). , Rn ). 64) becomes a standard linear mapping. 65), the stacking expression of a matrix polynomial may also be obtained. 2 Let X be a square matrix and p(x) be a polynomial, expressible as p(x) = q(x)x + p0 .

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

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