1.非线性复杂系统的预测、分析与控制

 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.

 Using real-world mutualistic networks of pollinators and plants as prototypical systems and taking into account biological constraints, we develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with a tipping point. If conditions are changing so as to approach a tipping point, the management strategy we describe can prevent sudden drastic changes and removal of the hysteresis. 

Is linear controllability relevant to nonlinear dynamical networks? We identify a common trait underlying both types of control: the nodal “importance”. For nonlinear and linear control, the importance is determined, respectively, by physical/biological considerations and the probability for a node to be in the minimum driver set. We study empirical mutualistic networks and a gene regulatory network, for which the nonlinear nodal importance can be quantified by the ability of individual nodes to restore the system from the aftermath of a tipping-point transition. We find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former large-degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly the irrelevance of linear controllability to these systems. 

2. 大尺度脑网络模型的构建与分析

How does functional modularity emerge in a multiregional cortex made with repeats of a canonical local circuit architecture? We investigated this question by focusing on neural coding of working memory, a core cognitive function. Here we report a general mechanism dubbed “bifurcation in space”, and show that its salient signature is spatially localized “critical slowing down” leading to an inverted V-shaped profile of neuronal time constants along the cortical hierarchy during working memory. The phenomenon is confirmed in connectome-based large-scale models of mouse and monkey cortices, offering an experimentally testable prediction to assess whether working memory representation is modular. Many bifurcations in space could explain the emergence of different activity patterns potentially deployed for distinct cognitive functions. This work demonstrates that a distributed mental representation is compatible with functional specificity as a consequence of macroscopic gradients of neurobiological properties across the cortex, suggesting a general principle for the brain’s modular organization.

3. 智能算法的可解释性

Focusing on a class of recurrent neural networks—reservoir computing systems, which have recently been exploited for model-free prediction of nonlinear dynamical systems—we uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized. In a three-dimensional representation of the error versus the time and spectral radius, the interval corresponds to the bottom region of a “valley.” Such a valley arises for a variety of spatiotemporal dynamical systems described by nonlinear partial differential equations, regardless of the structure and the edge-weight distribution of the underlying reservoir network. We also find that, while the particular location and size of the valley depend on the details of the target system to be predicted, the interval tends to be larger for undirected than for directed networks.

4. 非线性数据的预测与分析

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has been about half dozen Lyapunov time. Is it possible to significantly extend the prediction time beyond what has been achieved so far? We articulate a scheme incorporating time-dependent but sparse data inputs into reservoir computing and demonstrate that such rare “updates” of the actual state practically enable an arbitrarily long prediction horizon for a variety of chaotic systems. A physical understanding based on the theory of temporal synchronization is developed.