NEWWAVE: New methods for analysing travelling waves in discrete systems with applications to neuroscience

NEWWAVE：分析离散系统中行波的新方法及其在神经科学中的应用

• 批准号: EP/Y027531/1
• 负责人: Alastair Rucklidge
• 金额: $ 25.55万
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY027531%2F1
• 关键词: NEWWAVE; New; methods; analysing; travelling

Patterns of animal colouration, biological tissues, vegetation patterns and the formation of crystals, as well as spatio-temporalpatterns such as travelling (water) waves, (laser) pulses and (electrical) spikes have captivated researchers in various fields of science for many decades. Project NEWWAVE puts forward a unique and unprecedented approach to studying such patterns in discrete, spatially-extended and delay-coupled systems of excitable and bistable units, which play an important role for neural signal propagation. Such systems can be obtained, for example, from discretisation of an underlying partial differential equation model, from the discreteness of the measured data, or from the microstructure of the medium. They can also be obtained bottom-up, from studying the response of single active unit to its neighbourhood, and large systems of coupled units are gaining more and more attention through the emergence of complex systems science and network science. The specific proposed research involves overcoming considerable mathematical and numerical challenges associated with time delays of mixed-type that appear when either (A) taking into account the finite speed of communication between discrete loci, or (B) imposing a TW ansatz (co-moving coordinates) on a discrete system. The projected results promise significant potential for innovating the bifurcation (qualitative changes) analysis of TWs in discrete systems and will advance our understanding of their dynamic repertoire through new analytical and numerical means, and by making the developed methods available as an open source library as part of the project. The techniques will be used to elucidate the functional role of travelling waves in the brain and, more specifically, the role of TWs in Parkinson's disease together with project collaborators in Neuroscience.

动物颜色、生物组织、植被模式和晶体形成的模式，以及行波（水）波、（激光）脉冲和（电）尖峰等时空模式，几十年来一直吸引着各个科学领域的研究人员。 NEWWAVE 项目提出了一种独特且前所未有的方法来研究可兴奋和双稳态单元的离散、空间扩展和延迟耦合系统中的此类模式，这些模式在神经信号传播中发挥着重要作用。例如，可以从基础偏微分方程模型的离散化、从测量数据的离散性或从介质的微观结构获得这样的系统。它们也可以自下而上地获得，通过研究单个活动单元对其邻近单元的响应，并且通过复杂系统科学和网络科学的出现，耦合单元的大型系统正在获得越来越多的关注。具体提出的研究涉及克服与混合型时间延迟相关的相当大的数学和数值挑战，这些挑战出现在（A）考虑离散基因座之间的有限通信速度，或（B）施加TW ansatz（共同移动坐标）在离散系统上。预计结果有望为离散系统中TW的分岔（质变）分析带来巨大的创新潜力，并将通过新的分析和数值手段，以及将开发的方法作为开源库的一部分，促进我们对其动态特性的理解。项目的。这些技术将与神经科学项目合作者一起用于阐明行波在大脑中的功能作用，更具体地说，行波在帕金森病中的作用。