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A Boolean network (BN) is well known as a discrete model for analysis and control of complex networks such as gene regulatory networks. Since complex networks are large-scale in general, it is important to consider model reduction. In this paper, we consider model reduction that the information on fixed points (singleton attractors) is preserved. In model reduction studied here, the interaction graph obtained from a given BN is utilized. In the existing method, the minimum feedback vertex set (FVS) of the interaction graph is focused on. The dimension of the state is reduced to the number of elements of the minimum FVS. In the proposed method, we focus on complement and absorption laws of Boolean functions in substitution operations of a Boolean function into other one. By simplifying Boolean functions, the dimension of the state may be further reduced. Through a numerical example, we present that by the proposed method, the dimension of the state can be reduced for BNs that the dimension of the state cannot be reduced by the existing method.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.5 pp.721-728

- Publication Date
- 2023/05/01

- Publicized
- 2022/10/24

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2022MAP0009

- Type of Manuscript
- Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)

- Category

Fuma MOTOYAMA

Hokkaido University

Koichi KOBAYASHI

Hokkaido University

Yuh YAMASHITA

Hokkaido University

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Fuma MOTOYAMA, Koichi KOBAYASHI, Yuh YAMASHITA, "Fixed Point Preserving Model Reduction of Boolean Networks Focusing on Complement and Absorption Laws" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 5, pp. 721-728, May 2023, doi: 10.1587/transfun.2022MAP0009.

Abstract: A Boolean network (BN) is well known as a discrete model for analysis and control of complex networks such as gene regulatory networks. Since complex networks are large-scale in general, it is important to consider model reduction. In this paper, we consider model reduction that the information on fixed points (singleton attractors) is preserved. In model reduction studied here, the interaction graph obtained from a given BN is utilized. In the existing method, the minimum feedback vertex set (FVS) of the interaction graph is focused on. The dimension of the state is reduced to the number of elements of the minimum FVS. In the proposed method, we focus on complement and absorption laws of Boolean functions in substitution operations of a Boolean function into other one. By simplifying Boolean functions, the dimension of the state may be further reduced. Through a numerical example, we present that by the proposed method, the dimension of the state can be reduced for BNs that the dimension of the state cannot be reduced by the existing method.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022MAP0009/_p

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@ARTICLE{e106-a_5_721,

author={Fuma MOTOYAMA, Koichi KOBAYASHI, Yuh YAMASHITA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Fixed Point Preserving Model Reduction of Boolean Networks Focusing on Complement and Absorption Laws},

year={2023},

volume={E106-A},

number={5},

pages={721-728},

abstract={A Boolean network (BN) is well known as a discrete model for analysis and control of complex networks such as gene regulatory networks. Since complex networks are large-scale in general, it is important to consider model reduction. In this paper, we consider model reduction that the information on fixed points (singleton attractors) is preserved. In model reduction studied here, the interaction graph obtained from a given BN is utilized. In the existing method, the minimum feedback vertex set (FVS) of the interaction graph is focused on. The dimension of the state is reduced to the number of elements of the minimum FVS. In the proposed method, we focus on complement and absorption laws of Boolean functions in substitution operations of a Boolean function into other one. By simplifying Boolean functions, the dimension of the state may be further reduced. Through a numerical example, we present that by the proposed method, the dimension of the state can be reduced for BNs that the dimension of the state cannot be reduced by the existing method.},

keywords={},

doi={10.1587/transfun.2022MAP0009},

ISSN={1745-1337},

month={May},}

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TY - JOUR

TI - Fixed Point Preserving Model Reduction of Boolean Networks Focusing on Complement and Absorption Laws

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 721

EP - 728

AU - Fuma MOTOYAMA

AU - Koichi KOBAYASHI

AU - Yuh YAMASHITA

PY - 2023

DO - 10.1587/transfun.2022MAP0009

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E106-A

IS - 5

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - May 2023

AB - A Boolean network (BN) is well known as a discrete model for analysis and control of complex networks such as gene regulatory networks. Since complex networks are large-scale in general, it is important to consider model reduction. In this paper, we consider model reduction that the information on fixed points (singleton attractors) is preserved. In model reduction studied here, the interaction graph obtained from a given BN is utilized. In the existing method, the minimum feedback vertex set (FVS) of the interaction graph is focused on. The dimension of the state is reduced to the number of elements of the minimum FVS. In the proposed method, we focus on complement and absorption laws of Boolean functions in substitution operations of a Boolean function into other one. By simplifying Boolean functions, the dimension of the state may be further reduced. Through a numerical example, we present that by the proposed method, the dimension of the state can be reduced for BNs that the dimension of the state cannot be reduced by the existing method.

ER -