SignificanceComplex systems in many fields, because of their intrinsic nonlinear dynamics, can exhibit a tipping point (point of no return) at which a total collapse of the system occurs. In ecosystems, environmental deterioration can lead to evolution toward a tipping point. To predict tipping point is an outstanding and extremely challenging problem. Using complex bipartite mutualistic networks, we articulate a dimension reduction strategy and establish its general applicability to predicting tipping points using a large number of empirical networks. Not only can our reduced model serve as a paradigm for understanding the tipping point dynamics in real world ecosystems for safeguarding pollinators, the principle can also be extended to other disciplines to address critical issues, such as resilience and sustainability.

In this paper, the initial value problem for a class of fractional differential equations is discussed, which generalizes the existent result to a wide class of fractional differential equations. Also the theoretical result established in the paper ensures the validity of chaos control of fractional differential equations. In particular, feed-back control of chaotic fractional differential equation is theoretically investigated and the fractional Lorenz system as a numerical example is further provided to verify the analytical result.

The specific expression of CDH5 in GSCs may contribute to GSC-derived neovasculogenesis in glioblastoma multiforme, especially under hypoxic conditions, revealing novel tumorigenic mechanisms contributed by GSCs.

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Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. Although several methods in traditional frameworks have been proposed to avoid such misinterpretations, there still is a lack of feasible methods for identifying direct causations from indirect ones in the challenging situation where the variables of the underlying dynamical system are non-separable and weakly or moderately interacting. Here, we solve this problem by developing a data-based, model-independent method of partial cross mapping based on an articulated integration of three tools from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation. We demonstrate our method by using data from different representative models and real-world systems. As direct causations are keys to the fundamental underpinnings of a variety of complex dynamics, we anticipate our method to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data.

SignificanceMaking accurate forecast or prediction is a challenging task in the big data era, in particular for those datasets involving high-dimensional variables but short-term time series points, and these datasets are omnipresent in many fields. In this work, a model-free framework, named as “randomly distributed embedding” (RDE), is proposed to accurately predict future dynamics based on such short-term but high-dimensional data. The RDE framework creates the distribution information from the interactions among high-dimensional variables to compensate for the lack of time points in real applications. Instead of roughly predicting a single trial of future values, this framework achieves the accurate prediction by using the distribution information.

Preoperative FMISO uptake is significantly correlated with the expression of VEGF in the tumour and might be used as a biomarker of antiangiogenic treatment in newly diagnosed malignant gliomas. However, caution is required because the correlation was weak and there was a large overlap of FMISO uptake between glioma with high and low VEGF expression. In addition, hypoxia determined by FMISO PET appears to be a suitable biomarker for predicting a highly malignant tumour and a poor prognosis in patients with malignant glioma.

Positive solutions of systems of Hammerstein integral equations are studied by using the theory of the fixed-point index for compact maps defined on cones in Banach spaces. Criteria for the fixed-point index of the Hammerstein integral operators being 1 or 0 are given. These criteria are generalizations of previous results on a single Hammerstein integral operator. Some of criteria are new and involve the first eigenvalues of the corresponding systems of linear Hammerstein operators. The existence and estimates of the first eigenvalues are given. Applications are given to systems of fractional differential equations with two-point boundary conditions. The Green's functions of the boundary value problems are derived and their useful properties are provided. As illustrations, the existence of nonzero positive solutions of two specific such boundary value problems is studied.