开关布尔网络的最小可观测性

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-19 DOI:10.1002/mma.10485

Yupeng Sun, Shihua Fu, Liyuan Xia, Jiayi Xu

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引用次数: 0

摘要

本文研究了开关布尔网络（SBN）的最小可观测性。首先，应用矩阵的半张量积（STP）方法，构建了一个并行扩展系统，在此基础上给出了检测 SBN 可观测性的必要条件和充分条件。其次，当 SBN 不可观测时，利用可达到集合法给出了获得所需测量值以使系统可观测的具体步骤；然而，这部分给出的测量值并不一定是最少的。然后，通过构建指标矩阵，进一步提出了确定最少测量次数的标准。最后，通过一个实例验证了新结果的有效性。

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Minimal observability of switching Boolean networks

In this paper, the minimal observability of switching Boolean networks (SBNs) is investigated. Firstly, applying the semi‐tensor product (STP) method of matrices, a parallel extension system is constructed, based on which a necessary and sufficient condition to detect the observability of the SBNs is given. Secondly, when an SBN is unobservable, the specific steps to obtain the required measurements to make the system observable are given using the set reachable method; however, the measurements given in this part are not necessarily the fewest. Then, a criterion for determining the minimum number of measurements is further proposed through a constructed indicator matrix. Lastly, the effectiveness of the new results is verified by an example.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.