Architecture for robust spatiotemporal dynamics in neuronal networks

神经科学中的一个主要挑战是理解大脑如何可靠地完成认知任务，尽管存在大量的内在变异性。认知任务通常需要协调的时空活动，实验者可以使用多个电极、电压敏感染料和光学技术来测量。这项研究项目的主要目标是开发数学工具，研究大脑中空间结构的网络如何在面对噪音时产生可靠的活动。具体地说，我们将感兴趣的是突触连接的空间结构如何与多个尺度上的噪声相互作用来影响网络活动。因此，将我们的理论与实验数据联系起来将需要在随机和非线性分析、多尺度方法和对称分叉理论方面发展新的技术。包含空间的神经元网络模型通常假设突触连接仅取决于神经元之间的距离。这样的动力系统往往是边际稳定的，因此解在存在噪声的情况下扩散。更现实的神经元连接模型不会产生这种退化。我们建议研究空间异质性如何提高或限制神经元网络的健壮性。我们将分析编码与工作记忆、决策和地点定位相关的神经活动的模型。我们的工作将为当前数学生物学的其他研究领域贡献数学方法，这些领域涉及分析噪声对空间扩展系统的影响。每天，人类都在做决定，使用记忆，在他们的环境中导航。大脑的空间结构活动是所有这些过程的基础。活动的空间局部化“突起”被认为编码了对空间位置的短期记忆。传播的活动波代表视觉输入和四肢的运动。这些活动模式一定是在充满噪音的大脑网络中产生的。尽管大脑很嘈杂，但我们忠实地执行认知任务。这是怎么发生的？我们将开发数学技术来解决这个主要问题。主要，我们将探索如何构建神经元网络以支持稳健的时空动力学。对认知过程的稳健性的洞察可以用来开发各种精神障碍的治疗方案。随着人类寿命的增长，阿尔茨海默氏症、痴呆症和帕金森氏症更常见。如果没有完善的理论，治疗是不可能的。我们对时空神经编码的分析还将有助于理解如何最好地设计多电极的空间阵列以用于神经假体等应用。

A major challenge in neuroscience is to understand how the brain reliably completes cognitive tasks, despite a great deal of intrinsic variability. Cognitive tasks often require coordinated spatiotemporal activity, which experimentalists can measure using multiple electrodes, voltage sensitive dye, and optical techniques. The main goal of this research project is to develop mathematical tools to study how spatially structured networks in the brain produce reliable activity in the face of noise. Specifically, we will be interested in how the spatial architecture of synaptic connections interacts with noise on multiple scales to influence network activity. Thus, linking our theory with experimental data will require the development of new techniques in stochastic and nonlinear analysis, multiscale methods, and symmetric bifurcation theory. Neuronal network models that incorporate space often assume synaptic connectivity depends only on the distance between neurons. Such dynamical systems tend to be marginally stable, so solutions diffuse in the presence of noise. More realistic models of neuronal connectivity do not produce such degeneracies. We propose to examine how spatial heterogeneity can improve or limit the robustness of neuronal networks. We will analyze models that encode neural activity linked to working memory, decision making, and place localization. Our work will contribute mathematical methods to other current research areas in math biology concerned with analyzing the effect of noise on spatially extended systems. Everyday, humans make decisions, use memory, and navigate their environment. Spatially structured activity in the brain underlies all these processes. Spatially localized "bumps" of activity are thought to encode short term memories of spatial position. Propagating waves of activity represent visual inputs and the movement of limbs. These activity patterns must be generated in networks of the brain that are fraught with noise. Despite the noisiness of the brain, we execute cognitive tasks faithfully. How does this happen? We will develop mathematical techniques to address this major question. Mainly, we will explore how neuronal networks can be structured to support robust spatiotemporal dynamics. Insight into the robustness of cognitive processes can be used to develop therapeutic solutions for various mental disorders. Alzheimer's, dementia, and Parkinson's present more commonly as human lifespans grow. Treatments are not possible without well-developed theory. Our analysis of spatiotemporal neural coding will also help understanding of how spatial arrays of multielectrodes should best be designed for applications like neural prosthetics.