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Although the tropical intraseaonal variability (TISV), as the most important predictability sources for subseasonal-to-seasonal (S2S) prediction, is dominated by Madden-Julian oscillation (MJO), its significant fraction does not always share the canonical MJO features, especially when the convective activity arrives at Maritime Continent. In this study, using principal oscillation pattern (POP) analysis on the combined fields of daily equatorial convection and zonal wind, two distinct leading TISV modes with relatively slower e-folding decay rates are identified. One is an oscillatory mode with the period of 51 days and e-folding time of 19 days, capturing the eastward propagating (EP) feature of the canonical MJO. The other is a non-oscillatory damping mode with e-folding time of 13.6 days, capturing a standing dipole (SD) with convection anomalies centered over the Maritime Continent and tropical central Pacific, respectively. Compared to the EP mode, the leading moisture anomalies at low level to the east of convection center are diminish for the SD mode, and instead, the strong negative anomalies of moisture and subsidence motion emerge in the tropical central Pacific area, which may be responsible for the distinct propagation features. Without filtering methods used, timeseries of the two POPs could be applied to the real-time monitoring of EP and SD events in the phase-space diagram. The two modes can serve as the simple and objective approach for a better characterization for diverse natures of TISV beyond the canonical MJO description, which may further shed light on dynamics of the TISV and its predictability. 

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.