Understanding Selective Recruitment in Neuronal Networks via Systems Theory

该项目将研究以特定互连结构为特征的系统的动力学，灵感来自神经细胞的特性。神经细胞模型通常实现某种类型的激活函数，其确定神经细胞如何响应来自其他神经细胞的输入刺激。本项目中研究的激活函数在结构的输入为正的情况下传递输入信号而不改变。然而，如果激活函数的输入为负，则输出为零。该激活函数产生了能够准确地表示真实的神经元的某些行为的神经细胞动力学模型。有强大的数学结果可用于这些模型。相比之下，具有基于指数的激活函数的神经细胞模型可能难以分析。该项目将创建新的数学工具来研究不同的子网络如何相互作用，要么抑制不需要的活动，要么同步和加强它们的反应。这些子网络可以按层次逐步构建成更复杂的结构。该项目将把这些网络与正常和异常的神经元回路联系起来。这些结果将有助于我们深入了解人类大脑的结构，也有助于构建可解释的工程网络，使其能够学习和适应。该项目将通过增加对生物神经系统的了解，并通过创建具有增强弹性和适应性的机器人系统来促进国民健康和福利。该项目还将通过本科生参与研究、研究生监督和课程制定、针对初中、高中、新生和转学生的外联活动、少数民族学生的参与和保留，该项目旨在解决大脑中选择性招募的实验证据与理论证据之间存在的差距。从系统和控制的角度来看，研究工作旨在开发一个数学框架来分析神经网络如何优化其计算能力，并揭示网络结构在塑造大脑动力学行为中的作用。这项研究旨在推进目前的知识，即大脑如何在每个时间间隔内选择相关的子网络并抑制其他子网络的活动，以及它如何有效地招募这些选定的子网络并协调与它们之间的信息传输。 研究计划是结构沿着以下相互关联的研究重点：（一）网络的稳定性和振荡的出现。该项目旨在深入表征网络结构的条件，确定其动态特性，特别是平衡点和极限环的存在性，唯一性和渐近稳定性;（ii）抑制控制和动态维数。该项目旨在描述两个网络之间的远程连接可以被一个网络用来动态地抑制另一个网络中的不同节点子集的机制。特别重要的一个方面是考虑生理相关的情况下，涉及前馈和反馈抑制，以及它们与网络的大小，结构和鲁棒性;（iii）区域间的连接和信息传输。在前两个重点所吸取的经验教训的基础上，该项目着手确定通过相干振荡进行信息传递的机制的特征。这涉及到神经元网络如何将信息编码和解码为振荡的研究，以及大脑的层次结构和区域间连接对它们的作用。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估而被认为值得支持。

This project will study the dynamics of systems characterized by a particular interconnection structure, inspired by properties of nerve cells. Nerve cell models typically implement some type of activation function, which determines how the nerve cell responds to input stimuli from other nerve cells. The activation function studied in this project passes an input signal without changes, if the input to the structure is positive. However, if the input to the activation function is negative, then the output is zero. This activation function gives rise to a model of nerve cell dynamics that is capable of accurately representing some behaviors of real neurons. There are powerful mathematical results available for these models. In contrast, nerve cell models with activation functions based on exponentials can be difficult to analyze. This project will create new mathematical tools to study how different subnetworks interact, either to suppress unwanted activity or to synchronize and reinforce their responses. These subnetworks can be built up hierarchically into progressively more complex structures. The project will relate these networks to both normal and abnormal neuronal circuits. The results will be of interest for the insight they provide into the architecture of the human brain, but also for constructing explainable engineered networks that can learn and adapt. This project will advance the national health and welfare by increasing understanding of biological neuronal systems, and by enabling the creation of robotic systems with enhanced resilience and adaptabilty. The project will also impact the training of a new generation of undergraduate and graduate students through undergraduate student involvement in research, graduate supervision and curriculum development, outreach targeted at middle, high school, incoming freshman and transfer students, involvement and retention of minority students, and broad dissemination activities.This project addresses the existing gap between the experimental evidence on selective recruitment in the brain and the theoretical understanding of the mechanisms that explain it. Taking a systems and controls perspective, the research effort aims to develop a mathematical framework to analyze how neuronal networks optimize their computational capabilities and unravel the role that network structure plays in shaping the dynamical behavior of the brain. This research seeks to advance the current knowledge on how the brain selects the relevant subnetworks during each time interval and suppresses the activity of others, and how it efficiently recruits those selected subnetworks and coordinates information transfer to and from them. The research plan is structured along the following interconnected research thrusts: (i) network stability and emergence of oscillations. The project seeks an in-depth characterization of the conditions on network structure that determine its dynamical properties, in particular, existence, uniqueness, and asymptotic stability of equilibrium points and limit cycles; (ii) inhibitory control and dynamic dimensionality. The project aims to characterize the mechanisms by which long-range connections between two networks can be used by one to dynamically inhibit different subset of nodes in the other. An aspect of particular importance is the consideration of physiologically-relevant scenarios involving feedforward and feedback inhibition, and their relation to network size, structure, and robustness; (iii) inter-regional connectivity and information transfer. Building on the lessons learned in the previous two thrusts, the project sets out to characterize the mechanisms of information transfer through coherent oscillations. This involves the study of ways in which neuronal networks can encode and decode information as oscillations and the role that the hierarchical structure and inter-regional connectivity of the brain has on them.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.