Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

Kobayashi, Koichi; Hiraishi, Kunihiko

doi:10.1109/tnnls.2016.2572063

Cited by 42 publications

(23 citation statements)

References 30 publications

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“…We may consider the case where a controller must be described by a certain Boolean function. In such a case, the algebraic representation using the STP and the matrix-based representation [54,55] Since BNs and PBNs are synchronous models, an extension to asynchronous models is important. Then, it is appropriate to utilize a Petri net representation.…”

Section: Open Problems In Control Theory Of Probabilistic Boolean Netmentioning

confidence: 99%

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%

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi

Hiraishi

2017

Algorithms

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“…As preliminaries, we explain a probabilistic Boolean network [3] and a matrix-based representation for a PBN [27].…”

Section: Preliminariesmentioning

confidence: 99%

“…In this subsection, we explain the outline of the matrix-based representation for PBNs [27]. Instead of this representation, we may use the matrix-based representation proposed in [5,6,14], where the semi-tensor product (STP) of matrices is used.…”

Section: Matrix-based Representation For Pbnsmentioning

confidence: 99%

“…For a BN, such a problem has been studied in [24,25]. For a PBN, such a problem has been studied in [26][27][28]. Comparing the method in [27] with other methods in [26,28], there is the advantage that the size of matrices manipulated in the procedure is smaller.…”

Section: Introductionmentioning

confidence: 99%

“…Comparing the method in [27] with other methods in [26,28], there is the advantage that the size of matrices manipulated in the procedure is smaller. Hence, we focus on the method in [27]. In this method, a linear programming (LP) problem with no objective function is solved.…”

Section: Introductionmentioning

confidence: 99%

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Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

2019

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A probabilistic Boolean network (PBN) is well known as one of the mathematical models of gene regulatory networks. In a Boolean network, expression of a gene is approximated by a binary value, and its time evolution is expressed by Boolean functions. In a PBN, a Boolean function is probabilistically chosen from candidates of Boolean functions. One of the authors has proposed a method to construct a PBN from imperfect information. However, there is a weakness that the number of candidates of Boolean functions may be redundant. In this paper, this construction method is improved to efficiently utilize given information. To derive Boolean functions and those selection probabilities, the linear programming problem is solved. Here, we introduce the objective function to reduce the number of candidates. The proposed method is demonstrated by a numerical example.

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Algebraic method of simplifying Boolean networks using semi‐tensor product of Matrices

Yan

Yue

Chen

2019

Asian Journal of Control

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The huge state space of large Boolean networks makes analysis and synthesis difficult. This paper, using a new matrix analysis tool called semi‐tensor product of matrices, to explain a simplification method of Boolean networks in a mathematical manner. The idea consists of two steps. First, remove the nodes whose logical dynamics are independent of themselves directly; second, use the logical functions (LFs) of the removed nodes to substitute for their corresponding variables in the LFs of other nodes; such nodes evolve directly with both themselves and the removed nodes. We discover that the simplified and original Boolean networks share some important topological structures such as attractor cycles, steady states and paths. An algebraic algorithm is provided to find all of the cycles and steady states of simplified Boolean networks. Finally we apply the results to the metastatic melanoma network to check the effect of the simplification method.

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Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities

Cited by 42 publications

References 30 publications

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

Algebraic method of simplifying Boolean networks using semi‐tensor product of Matrices

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