Singular Boolean networks: Semi-tensor product approach

Feng, Jun‐e; Yao, Juan; Cui, Peng

doi:10.1007/s11432-012-4666-8

Cited by 42 publications

(38 citation statements)

References 20 publications

(47 reference statements)

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“…The solvability theorems we obtained above are different from the results in [24] and we can see they are suitable for the case that the solution of SBNs is not unique for some initial value.…”

Section: Remarkcontrasting

confidence: 60%

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Topological structure and the disturbance decoupling problem of singular Boolean networks

Meng

Feng

2014

IET Control Theory & Applications

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The general singular Boolean networks are proposed in this study, motivated by the algebraic form of dynamicalgebraic Boolean networks via the semi-tensor product of matrices. First, one of the most important problems for this kind of networks, solvability problem, is discussed. Then, in order to calculate the fixed points and cycles, the transition matrix of a singular Boolean network is defined, which contains all the state transferring information. At last, the general singular Boolean control networks are considered with their solvability and the disturbance decoupling problem is presented and solved by a constant control. Illustrative examples are given to show the feasibility of the results.

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Section: Remarkcontrasting

confidence: 60%

“…The definition of fixed points and cycles of SBN (13) is similar to that in [24]. However, the difference is that the fixed points and cycles are assumed to be in the admissible condition set C.…”

Section: Remarkmentioning

confidence: 99%

Topological structure and the disturbance decoupling problem of singular Boolean networks

Meng

Feng

2014

IET Control Theory & Applications

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“…In recent years, the STP has been exploited by a wide range of applications: in nonlinear system control for structural analysis and control of Boolean networks [23,24], in biological systems as a solution to Morgan's Problem [25], in a linear system for nonlinear feedbackshift registers [26,27], etc. However, we have not yet seen publicly reported applications for the STP in the field of CS, to the best of our knowledge.…”

Section: Semi-tensor Productmentioning

confidence: 99%

Low storage space for compressive sensing: semi-tensor product approach

Wang

Ruan

et al. 2017

J Image Video Proc.

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Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

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“…Up to now, many fundamental results have been presented for the analysis and control of Boolean networks [13][14][15][16][17][18][19][20][21], the coloring problem [22], the design of shifting register [23], the fault detection [24], and so on. In addition, since the dynamics of a finite game can be modeled as a logical network [25], the semi-tensor product method has also been applied to the study of game theory [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Stable degree analysis for strategy profiles of evolutionary networked games

Guo

Wang

2016

Sci. China Inf. Sci.

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In this paper, we investigate the stable degree of strategy profile for evolutionary networked games by using the semi-tensor product method, and present a number of new results. First, we propose the concept of k-degree stability for strategy profiles based on a normal evolutionary networked game model. Second, using the semi-tensor product of matrices, we convert the game dynamics with "best imitate" strategy updating rule into an algebraic form. Third, based on the algebraic form of the game, we analyzed the stable degree of strategy profile, and proposed two necessary and sufficient conditions for the k-degree stability of strategy profile. Furthermore, we discuss the computation problem of the transient time within which a disturbed strategy profile can be restored, and also establish an algorithm for the verification of the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained in this paper are very effective.

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Singular Boolean networks: Semi-tensor product approach

Cited by 42 publications

References 20 publications

Topological structure and the disturbance decoupling problem of singular Boolean networks

Topological structure and the disturbance decoupling problem of singular Boolean networks

Low storage space for compressive sensing: semi-tensor product approach

Stable degree analysis for strategy profiles of evolutionary networked games

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