Coordination Funds

本单元的重点仍然是分析复杂网络上的动态过程，它们的使用，它们的平衡，以及它们意想不到的，潜在的灾难性后果，通过计算理论的严格分析机制。21世纪的计算机科学面临着应对复杂互动的必要性，这些互动不是由有目的的权威设计的，而是由自然、经济或社会力量塑造的。我们迫切需要工具来模拟这种复杂的相互作用，在他们身上展开的过程，他们可能达到的平衡，以及模拟这些过程的算法工具。这个研究小组的首要目标是开发这些工具。在第二阶段，该单位将调整研究努力，在一套及时和具有挑战性的方向上工作。它将保持建模网络过程，动力学和协议的设计和分析，以及仿真和实验的混合。第二阶段探讨的一个中心方面是网络的时间演化。虽然各种类型的静态随机图模型已经成为近三十年来网络科学的支柱，但这些模型在建模方面有明显的局限性，例如，接触网络需要时间轴。目前尚不清楚网络科学的主要假设——跨不同背景的网络表现出相似的基本特性——是否也适用于时间网络。另一个新的方面是亚稳态，即有吸引力的非平衡状态的存在，可能会在很长一段时间内捕获动力学。第三个新方面是结构网络特性的作用，与细粒度复杂性理论有关。潜在的问题是，结构图论的思想在多大程度上可以取代概率建模假设。

The focus of this unit remains the analysis of dynamical processes on complex networks, their uses, their equilibria, and their unintended, potentially cataclysmic consequences, by means of the rigorous analytical machinery of the theory of computing. Computer science in the 21st century faces the necessity to cope with complex interactions that, rather than being designed by a purposeful authority, are shaped by natural, economical, or social forces. We urgently require tools to model such complex interactions, the processes that unfold on them, the equilibria that they may attain as well as the algorithmic tools to simulate such processes. The overarching aim of this research group is to develop these tools. In the second phase, the unit will adjust the research efforts to work on a set of timely and challenging directions. It will maintain a mixture of modeling network processes, design and analysis of dynamics and protocols, as well as simulation and experiments. A central aspect explored in the second phase is the temporal evolution of networks. While static random graph models of various types have been the mainstay of network science for nearly three decades, these models have obvious limitations when it comes to modelling, e.g., contact networks, which require a time axis. At present it is far from clear whether the main hypothesis of network science -- that networks across different contexts exhibit similar fundamental properties -- holds true of temporal networks as well. A further new aspect is metastability, i.e., the presence of attractive out-of-equilibrium states that may trap dynamics for an extraordinarily long period of time. A third new aspect is the role of structural network properties, in connection with fine-grained complexity theory. The underlying question is to what extent ideas from structural graph theory can replace probabilistic modelling assumptions.