Mathematical Sciences: Modeling of Neural Populations

为了了解大量神经元的功能，研究人员将开发数学工具来描述和分析集体网络行为。将开发和研究解释大型神经群体中放电模式的时空结构的模型。群体行为将与单个神经元的电学和几何属性联系在一起，并源于这些属性。将使用简化方法来简化分析，同时保留不同程度的细节。缆索理论的新发展将被用来探索树突结构和突触位置对输入整合的影响。一种新开发的基于电导的神经元模型的简化方案将允许离子电流的动态被包括在内，并在尖峰速率和模式中反映出来。将研究射击率模型和探索人口射击的时间结构的模型。大脑中几乎所有的认知功能都是由大量神经元共同完成的。要了解这些认知过程是如何工作的，需要开发描述和分析大量神经元群体行为的技术。这个项目将使用数学和统计方法来研究大量神经元的动力学，特别是将关于单个神经元的属性及其突触连接的知识扩展到完整的神经网络的问题。

To understand how large populations of neurons function, the investigator will develop mathematical tools for describing and analyzing collective network behavior. Models that account for the spatial and temporal structure of firing patterns in large neural populations will be developed and studied. Population behavior will be tied to and derived from the electrical and geometric properties of individual neurons. Reduction methods will be used to streamline the analysis while retaining varying degrees of detail. New developments in cable theory will be used to explore the effects of dendritic structure and synaptic placement on input integration. A newly developed reduction scheme for conductance-based neuron models will allow the dynamics of ionic currents to be included and reflected in spiking rates and patterns. Both firing-rate models and models that explore the temporal structure of population firing will be investigated. Almost all of the cognitive functions in the brain are performed by large population of neurons working collectively. To understand how these cognitive processes work requires developing techniques for describing and analyzing the behavior of large neuronal populations. This project will use mathematical and statistical methods to study the dynamics of large populations of neurons, focusing in particular on the problem of extending knowledge about the properties of single neurons and their synaptic connections to full neural networks.