IEICE TRANSACTIONS on Fundamentals
Fixed Point Preserving Model Reduction of Boolean Networks Focusing on Complement and Absorption Laws
Summary :
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
Authors
Fuma MOTOYAMA
Hokkaido University
Koichi KOBAYASHI
Hokkaido University
Yuh YAMASHITA
Hokkaido University
Keyword
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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},}
Copy
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 -
English
