- 著者
- Makito Oku
- 出版者
- The Institute of Electronics, Information and Communication Engineers
- 雑誌
- Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)
- 巻号頁・発行日
- vol.14, no.2, pp.242-253, 2023 (Released:2023-04-01)
- 参考文献数
- 18
Critical transitions and early warning signals are gaining attention in various fields such as ecology, climatology, and economics. However, quantitative estimation of the critical transition probability remains difficult. In this study, I propose a method to estimate the critical transition probability. It is based on a previous method using quadratic polynomial approximation, and skewness filtering is added as a reject option. The proposed method is applied to May model, a mathematical model of an ecosystem, as an example case. The results of numerical simulations show that the proposed method has much better precision than the previous method without skewness filtering, achieving a relative error of approximately ±50% for the mean escape time.
- 著者
- Makito Oku Kazuyuki Aihara
- 出版者
- The Institute of Electronics, Information and Communication Engineers
- 雑誌
- Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)
- 巻号頁・発行日
- vol.9, no.2, pp.166-184, 2018 (Released:2018-04-01)
- 参考文献数
- 49
- 被引用文献数
- 18
In this paper, we analyze the relation between the stability of a noisy dynamical system based on linear approximation and the covariance matrix of its stationary distribution. We reformulate the theory of dynamical network biomarkers in terms of the covariance matrix and clarify the limiting behavior of the covariance matrix when a dynamical system approaches a bifurcation point. We also discuss the relation between the Jacobian matrix and principal component analysis. An application to a simple nonlinear network model is also demonstrated.
- 著者
- Makito Oku
- 出版者
- Information Processing Society of Japan
- 雑誌
- IPSJ Transactions on Bioinformatics (ISSN:18826679)
- 巻号頁・発行日
- vol.12, pp.9-16, 2019 (Released:2019-03-25)
- 参考文献数
- 16
- 被引用文献数
- 3
In this paper, I propose two novel methods for extracting synchronously fluctuated genes (SFGs) from a transcriptome data. Variability and synchrony in biological signals are generally considered to be associated with the system's stability in some sense. However, a standard method for extracting SFGs from a transcriptome data with high reproducibility has not been established. Here, I propose two novel methods for extracting SFGs. The first method has two steps: selection of remarkably fluctuated genes and extraction of synchronized gene clusters. The other method is based on principal component analysis. It has been confirmed that the two methods have high extraction performance for artificial data and a moderate level of reproducibility for real data. The proposed methods will help to extract candidate genes related to the stability and homeostasis in living organisms.