By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
Research and keep watch over of Boolean Networks provides a scientific new method of the research of Boolean keep an eye on networks. the elemental software during this procedure is a singular 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 approach. within the mild of this linear expression, definite significant concerns pertaining to Boolean community topology – mounted issues, cycles, brief instances and basins of attractors – might be simply printed via a collection of formulae. This framework renders the state-space method of dynamic keep an eye on platforms acceptable to Boolean keep an eye on networks. The bilinear-systemic illustration of a Boolean keep an eye on community makes it attainable to enquire easy regulate difficulties together with controllability, observability, stabilization, disturbance decoupling and so on.
Read Online or Download Analysis and Control of Boolean Networks: A Semi-tensor Product Approach PDF
Similar system theory books
Easy-to-follow studying constitution makes absorption of complex fabric as pain-free as attainable Introduces entire theories for balance and value monotonicity for restricted and non-linear platforms in addition to for linear structures In co-ordination with MATLAB® records to be had from springeronline. com, workouts and examples supply the coed extra perform within the predictive regulate and filtering recommendations provided
This publication is an advent into the optimization tools of operations examine - and past. With its transparent presentation, easy-to-read notation and routines, it presents an outstanding starting place and serves as a reference paintings even after commencement from collage.
During this unified account of the mathematical concept of disbursed parameter platforms (DPS), the authors conceal all significant facets of the keep an eye on, estimation, and identity of such platforms, and their program in engineering difficulties. the 1st a part of the booklet is dedicated to the elemental leads to deterministic and stochastic partial differential equations, that are utilized to the optimum keep watch over and estimation theories for DPS.
Workforce approach to information dealing with (GMDH) is a regular inductive modeling technique outfitted at the ideas of self-organization. due to the fact that its advent, inductive modeling has been built and utilized to complicated structures in parts like prediction, modeling, clusterization, procedure identity, in addition to information mining and information extraction applied sciences, to a number of fields together with social technology, technological know-how, engineering, and medication.
- Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems (Cambridge Lecture Notes in Physics)
- Discrete, Continuous, and Hybrid Petri Nets
- Distributed Systems with Persistent Memory: Control and Moment Problems
- Coexistence and Persistence of Strange Attractors
Additional resources for Analysis and Control of Boolean Networks: A Semi-tensor Product Approach
A question which then naturally arises is how to arrange three-dimensional data. A cubic matrix approach has been proposed for this purpose [1, 2] and has been used in some statistics problems [8–10], but, in general, has not been very successful. , on paper), (2) the conventional matrix product does not apply, hence some new product rules have to be produced, (3) it is very difficult to generalize this approach to even higher-dimensional cases. The basic idea concerning the semi-tensor product of matrices is that no matter what the dimension of the data, they are arranged in one- or two-dimensional form.
Its rows and columns are labeled by double index (i, j ), the columns are arranged by the ordered multi-index Id(i, j ; m, n), and the rows are arranged by the ordered multi-index Id(j, i; n, m). The element at position [(I, J ), (i, j )] is then I,J = w(I J ),(ij ) = δi,j 1, I = i and J = j, 0, otherwise. 16 1. Letting m = 2, n = 3, the swap matrix W[m,n] can be constructed as follows. Using double index (i, j ) to label its columns and rows, the columns of W are labeled by Id(i, j ; 2, 3), that is, (11, 12, 13, 21, 22, 23), and the rows of W are labeled by Id(j, i; 3, 2), that is, (11, 21, 12, 22, 13, 23).
Ik and arranged as follows: Let it , t = 1, . . , k, run from 1 to nt with the order that t = k first, then t = k − 1, and so on, until t = 1. ,βk if and only if there exists 1 ≤ j ≤ k such that αi = β i , i = 1, . . , j − 1, αj < βj . If the numbers n1 , . . , nk of i1 , . . , ik are equal, we may use Id(i1 , . . , ik ; n) := Id(i1 , . . , ik ; n, . . , n). If ni are obviously known, the expression of Id can be simplified as Id(i1 , . . , ik ) := Id(i1 , . . , ik ; n1 , . . , nk ).