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Theory of threshold-linear networks and combinatorial neural codes.

阈值线性网络和组合神经代码的理论。

基本信息

批准号：
1516881
负责人：
Carina Curto
金额：
$ 15万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-08-01 至 2019-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1516881&HistoricalAwards=false
关键词：
Theory threshold linear networks combinatorial

项目摘要

How do connections between neurons store memories and shape the dynamics of neural activity in the brain? How do firing patterns of neurons represent our sensory experiences? The advent of technologies that facilitate simultaneous recordings of large populations of neurons present new opportunities to answer these classical questions of neuroscience. There are mathematical models that are frequently used in network simulations and data analyses that can be employed, but whose mathematical properties are still poorly understood. To guide these efforts, a better understanding of theoretical models of recurrent networks and population codes is essential. This research will focus on two such examples: threshold-linear networks and combinatorial neural codes. The goal is to produce major advances in the mathematical theory of these models, with an eye towards neuroscience applications. Part of the research will involve the analyses of neural activity in the cortex and hippocampus, in collaboration with experimentalists. Despite the focus on neuroscience, the mathematical results have the potential to be sufficiently general so as to be useful in a variety of broader contexts in the biological and social sciences.A threshold-linear network is a common firing rate model for a recurrent network, with a threshold nonlinearity. These networks generically exhibit multiple stable fixed points, and multistability makes them attractive as models for memory storage and retrieval. Preliminary results have shown that the equilibria possess a rich combinatorial structure, and can be analyzed using ideas from classical distance geometry. The first project will build on this understanding in order to develop a more complete picture of the structure of fixed points and higher-dimensional attractors of these networks. A combinatorial neural code is a collection of binary patterns for a population of neurons. The second project will develop an algebraic classification of combinatorial codes, using the recently developed framework of the neural ring. The neural ring encodes information about a neural code in a manner that makes properties such as receptive field organization most transparent. The resulting methods will be tested and refined using electrophysiological recordings of place cells in the hippocampus. This research will also generate new and interesting problems at the interface of neuroscience with applied algebra, combinatorics, and geometry.

神经元之间的连接如何存储记忆并塑造大脑中神经活动的动力学？神经元的放电模式如何代表我们的感官体验？促进同时记录大量神经元的技术的出现为回答神经科学的这些经典问题提供了新的机会。有一些数学模型经常用于网络模拟和数据分析，但其数学性质仍然知之甚少。为了指导这些努力，更好地理解经常性网络和人口代码的理论模型是必不可少的。本研究将集中在两个这样的例子：阈值线性网络和组合神经代码。目标是在这些模型的数学理论方面取得重大进展，并着眼于神经科学应用。部分研究将涉及与实验学家合作分析皮层和海马体的神经活动。尽管重点放在神经科学上，但数学结果具有足够的普遍性，以便在生物学和社会科学的各种更广泛的背景下有用。阈值线性网络是递归网络的常见发射率模型，具有阈值非线性。这些网络通常表现出多个稳定的不动点，多稳定性使它们成为记忆存储和检索的模型。初步结果表明，平衡具有丰富的组合结构，并可以使用经典距离几何的思想进行分析。第一个项目将建立在这种理解的基础上，以便更完整地了解这些网络的不动点和高维吸引子的结构。组合神经代码是神经元群体的二进制模式的集合。第二个项目将使用最近开发的神经环框架开发组合代码的代数分类。神经环以一种方式编码关于神经代码的信息，这种方式使得诸如感受野组织之类的属性最透明。所产生的方法将进行测试，并使用在海马定位细胞的电生理记录完善。这项研究也将产生新的和有趣的问题，在接口的神经科学与应用代数，组合数学和几何。