Complex systems in biology, ecology, economics and many other fields often undergo slow changes affected by various external factors, whose persistent effects sometimes result in drastic or qualitative changes of system states from one stable state (i.e., the before-transition state) to another stable state (i.e., the after-transition state) through a pre-transition state. Data observed from real-world systems are usually intrinsically or extrinsically convoluted with big noise, for which the existing approaches may fail. Actually, when a system is constantly fluctuated by strong perturbations, the state transition may emerge stochastically far before the deterministic bifurcation, and strong nonlinearities brought by the big noise will violate the assumptions of many existing methods, such as critical slowing-down (CSD) and spectral analysis.
To address this issue, Prof. CHEN Luonan and his group from Key Laboratory of Systems Biology, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences developed a new method for identifying early-warning signals of critical transitions with strong noise by dynamical network marker (DNM) or dynamical network biomarker (DNB) in biology. In this method they designed a model-free computational strategy that making big noise smaller by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations.
They applied the method on three real datasets, i.e., genomic data of lung injury induced by carbonyl chloride inhalation exposure from NCBI database, the ecological data on a critical transition to a eutrophic lake state and the financial data on the bankruptcy of Lehman Brothers. The successful application showed the advantages of the distribution-embedding scheme: (i) by increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, new data are generated in a higher-dimensional space but with much smaller noise; (ii) on the basis of the new data in a higher-dimensional space, the dynamical network marker (DNM) in general fields or dynamical network biomarker (DNB) in biology works effectively and efficiently in detecting the early-warning signal of the critical transition.
This work entitled “Identifying early-warning signals of critical transitions with strong noise by dynamical network markers” was published in Scientific Reports on December 9, 2015. This work was supported by the grants from the Chinese Academy of Sciences and the National Natural Science Foundation of China.
CONTACT:
CHEN Luonan;
Key Laboratory of Systems Biology, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences
Shanghai 200031, China.
E-mail: lnchen@sibs.ac.cn
Scheme of probability distribution embedding. (a) When the system is under small noise, the critical point of the system is near a bifurcation point of the corresponding deterministic system. (b) When the system is under big noise, the critical transition takes place much earlier than that of the deterministic system due to strong fluctuations. (c) By moment expansion, the state-dynamics under big noise is transformed to the probability distribution-dynamics with much smaller noise but in a higher-dimensional space (e.g., a two-moment-variables system), for which the critical point is near the bifurcation of the reconstructed high-dimensional system. (d-g) The moment-expanding strategy decreases the fluctuation of the data, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. (Image provided by Prof. CHEN Luonan’s group)
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