Structural Monostability of Activation-Inhibition Boolean Networks

Azuma, Shun‐ichi; Yoshida, Takahiro; Sugie, Toshiharu

doi:10.1109/tcns.2015.2485440

Cited by 52 publications

(48 citation statements)

References 27 publications

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“…In [22], controllability of BNs is characterized using a time sequence of graph structure. In [16], singleton attractors (fixed points) of BNs are characterized from graph structure only. In [52,53], a feedback vertex set of a graph is focused.…”

Section: Open Problems In Control Theory Of Probabilistic Boolean Netmentioning

confidence: 99%

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Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi

Hiraishi

2017

Algorithms

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Abstract:Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs), which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs) are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.

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Section: Open Problems In Control Theory Of Probabilistic Boolean Netmentioning

confidence: 99%

“…In the last decade, many results on control of BNs and PBNs have been obtained so far (see, e.g., [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]). Especially, analysis and control methods using the semi-tensor product (STP) method have been widely studied (see, e.g., [33][34][35][36][37][38][39][40][41][42][43]).…”

Section: Introductionmentioning

confidence: 99%

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi

Hiraishi

2017

Algorithms

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“…The main contributions of this paper are as follows: The structural‐equivalent BNs are converted into algebraic forms by using the STP, which facilitates the structural stability analysis. Some necessary and sufficient conditions are presented for the structural monostability and structural cycle‐stability of BNs, which are easy to check via MATLAB. Compared with Azuma et al, the new conditions are applicable to BNs with arbitrary network topology structure. …”

Section: Introductionmentioning

confidence: 99%

“…It should be pointed out that in practical gene regulatory networks, the network structure is easily known, but the node dynamics are often completely or partially unknown. Considering this fact, Azuma et al proposed the concept of structural stability for BNs and presented several necessary and sufficient conditions for the structural monostability and oscillatority of BNs. However, Azuma et al only considered the structural stability of BNs with/without a fixed point.…”

Section: Introductionmentioning

confidence: 99%

“…Considering this fact, Azuma et al proposed the concept of structural stability for BNs and presented several necessary and sufficient conditions for the structural monostability and oscillatority of BNs. However, Azuma et al only considered the structural stability of BNs with/without a fixed point. For BNs with a cycle of length greater than 1, to our best knowledge, there exist fewer results to study the structural cycle‐stability of BNs.…”

Section: Introductionmentioning

confidence: 99%

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Structural stability analysis of gene regulatory networks modeled by Boolean networks

Liang

Zhao

et al. 2019

Math Methods in App Sciences

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This paper studies the structural monostability and structural cycle‐stability of Boolean networks (BNs). Firstly, the structural‐equivalent Boolean networks are converted to the algebraic forms by using the semitensor product of matrices. Secondly, the concepts of structural monostability and structural cycle‐stability for Boolean networks are proposed. On the basis of the algebraic forms of structural‐equivalent Boolean networks, some necessary and sufficient conditions are presented for the structural monostability and structural cycle‐stability of Boolean networks. Finally, an illustrative example is worked out to show the effectiveness of the obtained results.

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State feedback controller design for anti‐synchronization of Boolean control networks: An event‐based idea

Tong

Liang

Chen

2019

Asian Journal of Control

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In this paper, we investigate the event‐based state feedback control for the anti‐synchronization of Boolean control networks (BCNs) under the configuration of drive‐response coupling. Two equivalence properties for the anti‐synchronization of BCNs are obtained by the algebraic representations of the logical dynamics. Based on the analysis of the event conditions, an algorithm is established to design the event‐based state feedback controller, and a necessary and sufficient condition guaranteeing the anti‐synchronization of the drive‐response coupled BCNs is formulated. An example is finally given to demonstrate the validity of the obtained results.

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Structural Monostability of Activation-Inhibition Boolean Networks

Cited by 52 publications

References 27 publications

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Structural stability analysis of gene regulatory networks modeled by Boolean networks

State feedback controller design for anti‐synchronization of Boolean control networks: An event‐based idea

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