Edge-based relative entropy as a sensitive indicator of critical transitions in biological systems.

BACKGROUND: Disease progression in biosystems is not always a steady process but is occasionally abrupt. It is important but challenging to signal critical transitions in complex biosystems. METHODS: In this study, based on the theoretical framework of dynamic network biomarkers (DNBs), we propose a model-free method, edge-based relative entropy (ERE), to identify temporal key biomolecular associations/networks that may serve as DNBs and detect early-warning signals of the drastic state transition during disease progression in complex biological systems. Specifically, by combining gene‒gene interaction (edge) information with the relative entropy, the ERE method converts gene expression values into network entropy values, quantifying the dynamic change in a biomolecular network and indicating the qualitative shift in the system state. RESULTS: The proposed method was validated using simulated data and real biological datasets of complex diseases. The applications show that for certain diseases, the ERE method helps to reveal so-called "dark genes" that are non-differentially expressed but with high ERE values and of essential importance in both gene regulation and prognosis. CONCLUSIONS: The proposed method effectively identified the critical transition states of complex diseases at the network level. Our study not only identified the critical transition states of various cancers but also provided two types of new prognostic biomarkers, positive and negative edge biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

Earthquake alerting based on spatial geodetic data by spatiotemporal information transformation learning.

Alerting for imminent earthquakes is particularly challenging due to the high nonlinearity and nonstationarity of geodynamical phenomena. In this study, based on spatiotemporal information (STI) transformation for high-dimensional real-time data, we developed a model-free framework, i.e., real-time spatiotemporal information transformation learning (RSIT), for extending the nonlinear and nonstationary time series. Specifically, by transforming high-dimensional information of the global navigation satellite system into one-dimensional dynamics via the STI strategy, RSIT efficiently utilizes two criteria of the transformed one-dimensional dynamics, i.e., unpredictability and instability. Such two criteria contemporaneously signal a potential critical transition of the geodynamical system, thereby providing early-warning signals of possible upcoming earthquakes. RSIT explores both the spatial and temporal dynamics of real-world data on the basis of a solid theoretical background in nonlinear dynamics and delay-embedding theory. The effectiveness of RSIT was demonstrated on geodynamical data of recent earthquakes from a number of regions across at least 4 y and through further comparison with existing methods.