Networks: Emergence and dynamics

该提案的主要目标是通过协调和发展帝国理工大学数学系、物理系和生物工程系的现有活动来建立理论复杂性科学的能力。为该项目聘请的RA将被安置在帝国理工大学的数学科学研究所（IMS）。IMS为应用于现实世界问题的数学科学的跨学科研究提供了一个场所。通过这种方式，该项目将受益于IMS主持的其他复杂活动，并在各个部门的研究人员之间建立创造性的合作。建议的研究将集中在网络动力学上，这个术语包括网络上的动力学和网络的动力学。将开发与统计力学、动力系统理论和随机过程相关的理论工具，以分析和描述网络结构与集体网络行为的出现之间的关系。特别是，这项研究将发展我们对导致特定网络结构的动态进化过程的理解，以及发生在这些网络上的动态过程的性质。理论模型将受到临床神经科学部门实验获得的功能性脑成像数据的启发。另一方面，理论研究将激励实验的发展。

The main objective of this proposal is capacity building in theoretical complexity science by coordinating and developing existing activities in the Departments of Mathematics, Physics and Bioengineering at Imperial. The RA hired for the project will be placed in the Institute for Mathematical Sciences (IMS) at Imperial. The IMS provides a venue for transdisciplinary research in mathematical sciences applied to real world problems. In this way the project will benefit from the other complexity activities hosted by the IMS as well as forging an inventive collaboration between researchers from various Departments. The proposed research will focus on network dynamics, a term that encompasses both dynamics on, and dynamics of, networks. Theoretical tools related to statistical mechanics, dynamical systems theory and stochastic processes will be developed to analyse and characterise the relationship between network structure and the emergence of collective network behaviour. In particular, the research will develop our understanding of the dynamical evolutionary processes leading to specific network structure and the properties of dynamical processes taking place on such networks. The theoretical modelling will be inspired by functional brain imaging data obtained experimentally by the Division of Clinical Neuroscience. The theoretical research will on the other hand motivate the experimental development.