Stimulus representation and spontaneous activity in recurrent networks

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。这项研究包括三个项目，将开发新的理论方法和实验预测哺乳动物大脑中的循环网络。前两个项目主要关注通过循环网络的刺激表征，而第三个项目侧重于自发活动。 项目1形式化和发展的代数几何框架，以前介绍了联合工作与弗拉基米尔伊茨科夫。其主要思想是将几何形状和拓扑结构与群体尖峰序列数据相关联-主要来自皮层和海马体的电生理记录。 项目2探索刺激空间拓扑结构和经常性网络连接之间的关系。 这个项目的目标是找到实验预测的情况下，无论是刺激空间结构或底层网络的拓扑结构是已知的经常性网络的连接。 项目3研究单个神经元的活动与局部网络的群体活动之间的相互作用。构建对世界的准确表征是大脑的基本功能之一。 当刺激与快乐或痛苦配对时，动物很快就学会了这种联系。 然而，我们也学习相同类型的刺激之间的（中性）关系。 举个例子，一个45度角的横杆看起来更接近于50度角的横杆，而不是完全垂直的横杆。 听到一对截然不同的纯音，似乎一个比另一个高。 我们并不把世界看作是一串不相关的刺激;相反，我们的大脑将不同类型的刺激组织成结构化的刺激空间。 不管与生存的直接关系如何，大脑尽可能多地反映外部世界的结构似乎是有益的。 这项研究的主要目标是提高我们对刺激空间如何通过大脑中的循环网络表示的理解。 为此，我们开发的想法和技术来自几何和拓扑结构，从神经科学实验中提取新的见解。 大脑如何表征世界是一个基本而古老的问题。 在理解神经回路的结构如何构成表征功能的基础方面取得的进展也可能为神经疾病的研究提供线索。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This research consists of three projects that will develop new theoretical approaches and experimental predictions about recurrent networks in the mammalian brain. The first two projects are primarily concerned with stimulus representation via recurrent networks, while the third project focuses on spontaneous activity. Project 1 formalizes and develops an algebra-geometric framework previously introduced in joint work with Vladimir Itskov. The main idea is to associate geometry and topology to population spike train data -- primarily from electrophysiological recordings in cortex and hippocampus. Project 2 explores the relationship between stimulus space topology and recurrent network connectivity. The goal of this project is to find experimental predictions about the connectivity of recurrent networks in cases where either the stimulus space structure or the topographic structure of the underlying network is known. Project 3 investigates the interaction between the activity of single neurons and the population activity of the local network.Building accurate representations of the world is one of the basic functions of the brain. When a stimulus is paired with pleasure or pain, an animal quickly learns the association. However, we also learn the (neutral) relationships between stimuli of the same type. For example, a bar held at a 45-degree angle seems closer to one held at 50 degrees than to a perfectly vertical one. Upon hearing a pair of distinct pure tones, one seems higher than the other. We do not perceive the world as a stream of unrelated stimuli; rather, our brains organize different types of stimuli into structured stimulus spaces. Regardless of immediate relevance to survival, it appears to be beneficial for the brain to reflect as much structure as possible of the outside world. The main goal of this research is to improve our understanding of how stimulus spaces are represented via recurrent networks in the brain. To this end, we develop ideas and techniques coming from geometry and topology to extract novel insights from neuroscience experiments. How the brain represents the world is a fundamental and age-old question. Progress in understanding how the structure of neural circuits underlies representational functions may also provide clues in the study of neurological disease.