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 develop into a robust instrument for describing and simulating mobile networks during which the weather behave in an on–off style. research and keep an eye on of Boolean Networks offers a scientific new method of the research of Boolean regulate networks. the elemental instrument during this method is a unique matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality could be expressed as a standard discrete-time linear approach. within the gentle of this linear expression, convinced significant matters pertaining to Boolean community topology – fastened issues, cycles, temporary occasions and basins of attractors – could be simply published via a suite of formulae. This framework renders the state-space method of dynamic keep an eye on platforms appropriate 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 keep watch over, and so on.

The booklet is self-contained, requiring simply wisdom of linear algebra and the fundamentals of the keep an eye on thought of linear platforms. It starts off with a quick creation to prepositional good judgment and the strategies and homes of the STP and progressing through the (bi)linear expression of Boolean (control) networks to disturbance decoupling and decomposition of Boolean regulate platforms. ultimately multi-valued common sense is taken into account as a extra detailed manner 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 e-book may be downloaded from http://lsc.amss.ac.cn/~dcheng/.

Analysis and keep watch over of Boolean Networks might be a basic reference for researchers in structures biology, regulate, structures technology and physics. The booklet used to be built for a quick direction for graduate scholars and is acceptable for that objective. laptop scientists and logicians can also locate this ebook 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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For instance, consider x124 . Let x124 = y241 . 7), we have p = (Λ1 − 1)N2 N3 + (Λ2 − 1)N3 + Λ3 = (2 − 1) × 4 × 2 + (4 − 1) × 2 + 1 = 8 + 6 + 1 = 15. Hence x124 = y241 = y15 = x15 . Consider x17 again. 6), we have p3 = p − 1 = 16, Λ3 = p3 %N3 + 1 = 1, p2 = [p3 /N3 ] = 8, Λ2 = p2 %N2 + 1 = 1, p1 = [p2 /N2 ] = 2, Λ1 = p1 %N1 + 1 = 3. Hence x17 = y17 = y311 = x131 . 1 The prisoner’s dilemma Semi-tensor Product of Matrices P1 \P2 A1 A2 A1 A2 −1, −1 0, −9 −9, 0 −6, −6 single-index. A matrix, as a set of 2-dimensional data, can certainly be converted into a set of 1-dimensional data.

Yn x1 , yn x2 , . . , yn xm )T = (x1 y1 , x2 y1 , . . , xm y1 , . . , x1 yn , x2 yn , . . , xm yn )T . They both consist of {xi yj }. However, in X ⊗ Y the elements are arranged in the order of Id(i, j ; m, n), while in Y ⊗ X the elements are arranged in the order of Id(j, i; n, m). 1 we have Y ⊗ X = W[m,n] (X ⊗ Y ). 46) It is easy to check that XY = X ⊗ Y , so we have Y X = W[m,n] XY. 47) The following proposition comes from the definition. 6 1. Let X = (xij ) be a set of data arranged as a column vector by the ordered multiindex Id(i, j ; m, n).

Am1 am2 · · · amn elements are labeled by two indices, i and j , where ai,j is the element of A located in the ith row and j th column. In this way, it is easy to connect the dimension of a set of data with the number of indices. We define the dimension of a set of data as follows. 1 A set of data, labeled by k indices, is called a set of k-dimensional data. ,ik | 1 ≤ ij ≤ nj , j = 1, 2, . . 1) is a set of k-dimensional data. The cardinal number of X, denoted by |X|, is |X| = n1 n 2 · · · n k .

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