Topology of Neural Coding in Recurrent Networks: Theory and Data Analysis

该项目发展了一种数学理论，将神经元群体的编码特性与它们所属的局部网络结构联系起来。一个重要的组成部分是分析由神经元网络表示的刺激空间的拓扑不变量，如同调群，以及它们如何约束底层网络的连通性。这需要一种将代数拓扑方法与更传统的动力系统模型相结合的方法。这项研究将产生关于支持刺激表征的网络结构的可测试预测，并将加深我们对网络结构和功能之间关系的理解。该理论将通过对行为动物的多单元电生理记录的分析来进行测试和指导。大脑是相互连接的神经回路的巨大集合。在许多脑区，重要的神经计算是由局部神经元网络完成的。然而，即使在研究最多的大脑区域，如海马体，对大脑局部循环回路的结构仍然知之甚少。相比之下，神经科学实验在揭示单个神经元的编码特性，以及最近在描述局部神经元回路中群体活动模式方面要成功得多。这项研究开发了一种数学理论，利用我们对神经元群体的表征特性的知识，以便更好地理解底层网络的结构。这些发现对神经回路在学习和记忆中的作用以及大脑如何组织知识产生了新的见解。对神经回路的基本认识的进展对于提高我们对被认为与神经回路功能障碍有关的学习障碍和疾病（如癫痫和精神分裂症）的理解至关重要。

This project develops a mathematical theory that relates the coding properties of neuronal populations to the structure of the local networks to which they belong. An important ingredient is the analysis of topological invariants, such as homology groups, of the stimulus spaces represented by networks of neurons, and how they constrain the connectivity of the underlying networks. This necessitates an approach that blends algebraic-topological methods with more traditional dynamical systems models. The research will produce testable predictions about the structure of networks that support stimulus representation, and will deepen our understanding of the relationship between network structure and function. The theory will be both tested and guided by the analysis of multi-unit electrophysiological recordings in behaving animals.The brain is a vast collection of interconnected neural circuits. In many brain areas, important neural computations are accomplished by local networks of neurons. However, the structure of local recurrent circuits in the brain is still poorly understood, even in the most studied brain areas such as the hippocampus. In contrast, neuroscience experiments have been much more successful in uncovering coding properties of individual neurons and, more recently, in characterizing patterns of population activity in local neuronal circuits. This research develops a mathematical theory that exploits our knowledge of the representational properties of neuronal populations in order to better understand the structure of the underlying networks. The findings yield new insight into the role of neural circuits in learning and memory, and of how the brain organizes knowledge. Progress in the basic understanding of neural circuits is essential for improving our understanding of learning disabilities and diseases (such as epilepsy and schizophrenia) that are believed to be related to the malfunction of neural circuits.