CIF: Small: Understanding Complexity in Markovian Interaction Networks: Self-Organization, Functional Stability, Robustness, and Evolutionary Behavior

科学家和工程师感兴趣的许多自然和人造系统都是由相互作用的单个元素组成的，通过特定的渠道，产生和调节适当的反应。例子包括化学反应网络、细胞（信号、转录和代谢）网络、药代动力学网络、流行病学网络、生态网络、社会网络、神经网络、多主体网络等。了解这种网络的基本特性和设计原理是一个令人兴奋和具有挑战性的研究问题，其解决方案需要开发新的理论和计算方法。更复杂的是，大多数相互作用网络的动力学本质上是非线性和随机的。因此，需要一种统一的方法来同时涵盖网络的确定性和随机方面，从而为各种交互网络的建模和分析提供共同的方法和方法。本研究的主要目标是发展一种通用的理论和计算方法来表征和分析具有马尔可夫动力学的非线性相互作用网络的复杂性。虽然复杂性可能难以直接表征，但本研究严格追求并量化了复杂性的普遍特征：自组织、功能稳定性、健壮性和进化行为。研究人员研究了一种势能景观视角，将景观的地形特征与这些基本网络属性联系起来。为了实现这一努力的主要目标的可行性和计算效率，正在开发新的工具来计算潜在的随机种群动态的概率分布的时间演变。然后提出了严格的数学，算法和计算方法来模拟马尔可夫相互作用网络的紧急行为和复杂性，以及通过概率灵敏度分析技术研究其功能稳定性和热力学鲁棒性。

Many natural and man-made systems of interest to scientists and engineers are composed of groups of individual elements interacting with each other, through specific channels, to produce and regulate appropriate responses. Examples include chemical reaction networks, cellular (signaling, transcriptional, and metabolic) networks, pharmacokinetic networks, epidemiological networks, ecological networks, social networks, neural networks, multi-agent networks, etc. Understanding the fundamental properties and design principles of such networks is an exciting and challenging research problem whose solution requires development of new theoretical and computational approaches. To complicate matters, the dynamics of most interaction networks are inherently nonlinear and stochastic. A unifying approach is thus needed to concurrently encompass the deterministic and stochastic aspects of networks that can lead to common approaches and methods for the modeling and analysis of a diverse body of interaction networks.The main goal of this research is to develop a general theoretical and computational approach for characterizing and analyzing complexity in nonlinear interaction networks with Markovian dynamics. While complexity may be difficult to characterize directly, this research rigorously pursues and quantifies the prevalent hallmarks of complexity: self-organization, functional stability, robustness, and evolutionary behavior. The investigators study a potential energy landscape perspective that relates topographic features of the landscape to these fundamental network properties. To achieve feasibility and computational efficiency of the main goals of this effort, new tools are being developed for computing the time evolution of the probability distribution of the underlying stochastic population dynamics. Rigorous mathematical, algorithmic, and computational approaches are then proposed for modeling the emergent behavior and complexity of Markovian interaction networks as well as for studying their functional stability and thermodynamic robustness by probabilistic sensitivity analysis techniques.