# 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.

**Read Online or Download Analysis and Control of Boolean Networks: A Semi-tensor Product Approach PDF**

**Best system theory books**

**Read e-book online Mathematical Ecology of Populations and Ecosystems PDF**

Inhabitants ecologists learn how births and deaths have an effect on the dynamics of populations and groups whereas surroundings ecologists examine how species keep an eye on the flux of strength and fabrics via meals webs and ecosystems. even if some of these procedures take place at the same time in nature, the mathematical frameworks bridging the 2 disciplines have built independently.

**Robot Navigation from Nature: Simultaneous Localisation, - download pdf or read online**

This pioneering publication describes the improvement of a robotic mapping and navigation approach encouraged by way of types of the neural mechanisms underlying spatial navigation within the rodent hippocampus. Computational types of animal navigation structures have ordinarily had restricted functionality whilst carried out on robots.

**Mihajlo D Mesarovic, Y. Takahara's General Systems Theory: Mathematical Foundations PDF**

During this ebook, we examine theoretical and functional facets of computing tools for mathematical modelling of nonlinear structures. a couple of computing concepts are thought of, reminiscent of tools of operator approximation with any given accuracy; operator interpolation innovations together with a non-Lagrange interpolation; tools of procedure illustration topic to constraints linked to suggestions of causality, reminiscence and stationarity; equipment of process illustration with an accuracy that's the most sensible inside of a given type of types; equipment of covariance matrix estimation;methods for low-rank matrix approximations; hybrid equipment in keeping with a mix of iterative systems and top operator approximation; andmethods for info compression and filtering less than filter out version may still fulfill regulations linked to causality and sorts of reminiscence.

**Download e-book for iPad: GMDH-Methodology and Implementation in C by Godfrey Onwubolu**

Crew approach to facts dealing with (GMDH) is a regular inductive modeling process equipped at the ideas of self-organization. considering its creation, inductive modeling has been built and utilized to advanced structures in components like prediction, modeling, clusterization, procedure identity, in addition to information mining and data extraction applied sciences, to numerous fields together with social technology, technological know-how, engineering, and medication.

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

**Sample text**

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.

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

by Steven

4.4