The Role of Decaying Inhibition in Forced Networks of Neurons

振荡神经元的强迫网络在神经系统中无处不在。虽然强迫酉振子已经被大量研究，但很少有研究周期性强迫对具有多个内自由度的振子网络的影响。了解这样的系统是理解大脑如何利用其节律动态在区域间传递信号的重要一步。这个项目中的网络几乎具有神经元网络的普遍特性：抑制呈指数衰减，反馈给网络的兴奋细胞。在这些项目中，抑制的衰减性质对于低维动力学的出现以及产生和分析网络现象简化模型的能力是重要的。最初的三个子项目涉及噪声、多个周期输入和提供与周期性强迫相互作用的额外时间尺度的内在电流。这项工作将把网络相互作用的性质，如衰减抑制，与不变流形理论的几何思想联系起来。其目的是产生一定程度的数学清晰度，这通常不是初始建模工作的一部分，并扩展可用于进一步研究强制网络的工具和概念集。该项目侧重于产生伽马（30-80赫兹）振荡和贝塔（12-30赫兹）振荡的网络，并对与这些节律相适应的神经元进行生理描述。神经系统的动态是认知功能的核心，但大脑如何利用其动态才刚刚开始被理解。神经系统的节律长期以来被认为与认知过程密切相关，包括感觉编码、注意力、学习、记忆和运动计划。对这种节律的研究，以及它们在大脑交流中的应用，是生理学和功能之间的一个很好的桥梁。这个项目处理的是神经元网络对周期性和其他输入的反应，就像从大脑其他部分到达的信号中看到的那样。该项目的目的是了解大脑网络如何处理它们的时间和空间编码输入。这项工作是在研究大脑节律的起源和意义的广泛倡议的背景下进行的。科佩尔是认知节律协作组织的创始人和现任负责人，该组织由二十多名波士顿高级研究人员组成，他们对神经活动的生理和动力学机制、它们在认知中的重要性、它们在精神分裂症、帕金森病和癫痫等神经系统疾病中的病理以及它们在麻醉中的变化感兴趣；它包括在体内和体外工作的实验人员，数学家，统计学家和医务人员，他们已经将数学研究的想法纳入临床实践。

Forced networks of oscillating neurons are ubiquitous in the nervous system. Although forced unitary oscillators have been heavily studied, there are very few studies of the effects of periodic forcing on networks of oscillators with multiple internal degrees of freedom. Understanding such systems is an essential step in understanding how the brain makes use of its rhythmic dynamics to communicate signals among regions. The networks in this project have an almost universal property of networks of neurons: there is exponentially decaying inhibition that feeds back to the excitatory cells of the network. In these projects, the decaying nature of the inhibition is important for the emergence of lower-dimensional dynamics and the ability to produce and analyze simplified models of network phenomena. The initial three subprojects concern noise, multiple periodic inputs, and intrinsic currents providing extra timescales that interact with periodic forcing. The work will relate the properties of network interaction, such as the decaying inhibition, to geometric ideas of invariant manifold theory. The aim is to produce a level of mathematical clarity that is not generally a part of initial modeling work, and to expand the set of tools and concepts available for further study of forced networks. The project focuses on networks producing gamma (30-80 Hz) oscillations and beta (12-30 Hz) oscillations, with physiological descriptions of the neurons appropriate to those rhythms.The dynamics of the nervous system are central to cognitive function, but how the brain makes use of its dynamics is barely beginning to be understood. Rhythms of the nervous system have long been known to be highly associated with cognitive processes including sensory coding, attention, learning, memory, and motor planning. The study of such rhythms, and their use in brain communication, is an excellent bridge between physiology and function. This project deals with the response of networks of neurons to periodic and other input, as would be seen from signals arriving from other parts of the brain. The purpose of the project is to understand how brain networks process their temporally and spatially coded inputs. This work is being done in the context of a broad initiative to study the origin and significance of brain rhythms. Kopell is the founder and current head of the Cognitive Rhythms Collaborative, a group of over two dozen Boston-based senior investigators interested in the physiological and dynamical mechanisms of neural activity, their importance in cognition, and their pathology in neurological diseases including schizophrenia, Parkinson's disease and epilepsy, as well as their changes in anesthesia; it includes experimentalists working in vivo and in vitro, mathematicians, statisticians and medical personnel, who are already incorporating ideas from the mathematical research into clinical practice.