Harvesting random embedding for high-frequency change-point detection in temporal complex systems.

Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal structures has become a tremendously significant mission, beneficial to fully understanding the underlying mechanisms of evolving systems, and adequately modeling and predicting the dynamics of the systems as well. In real-world applications, due to a lack of prior knowledge on the explicit equations of evolving systems, an open challenge is how to develop a practical and model-free method to achieve the mission based merely on the time-series data recorded from real-world systems. Here, we develop such a model-free approach, named temporal change-point detection (TCD), and integrate both dynamical and statistical methods to address this important challenge in a novel way. The proposed TCD approach, basing on exploitation of spatial information of the observed time series of high dimensions, is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner, which cannot be directly achieved by using the existing methods and techniques. Practical effectiveness is comprehensively demonstrated using the data from the representative complex dynamics and real-world systems from biology to geology and even to social science.

Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately.

Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

[Stability of Soil Aggregates at Different Altitudes in Qinling Mountains and Its Coupling Relationship with Soil Enzyme Activities].

To explore changes in soil aggregate stability along an elevation gradient, and its regulating factors, soil samples were taken from the 0-10 cm surface layer at 3 different elevations on Taibai Mountain. We measured and analyzed the distribution of soil aggregates, physical and chemical properties, microbial biomass, and extracellular enzymes. The results showed that: ① the soil aggregates from the 3 elevations had mean weight diameters (MWD) of 2.17 mm, 1.83 mm, and 1.82 mm (increasing elevation), and geometric mean diameters (GMD) of 1.66 mm, 1.39 mm, and 1.32 mm, respectively. ② The change in soil aggregate stability along an elevation gradient was regulated by extracellular enzymes in the soil, in particular, the LAP in soil meso-aggregate and the BG in soil micro-aggregate. ③ Microorganisms can alleviate the N limitation at high elevations by adjusting the relative production of extracellular enzymes and altering nutrient utilization efficiency, which also changes soil aggregate stability along an elevation gradient. The results of this study have important scientific significance for soil quality evaluation and ecological environment protection in Taibai Mountain.

Failure of parameter identification based on adaptive synchronization techniques.

In this paper, several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so-called adaptive synchronization techniques. These failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit, but also when this orbit is deliberately designed to be chaotic. The reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved. Moreover, synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally Lipschitz. In addition, unknown parameter identification is studied in coupled systems with time delays.