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， 分析集体网络行为。 模型解释了 大范围放电模式的时空结构 将开发和研究神经群体。 人口 行为将与电气和 单个神经元的几何特性。 还原方法 将用于简化分析，同时保留不同的 细节的程度。 电缆理论的新发展将是 用于探索树突结构和突触的影响， 输入集成的布局。 新开发的还原 基于电导的神经元模型的方案将允许 离子电流的动力学将被包括和反映在 峰值速率和模式 发射率模型和模型 探索人口解雇的时间结构将是 研究了 大脑中几乎所有的认知功能 是由大量神经元工作完成的 集体的 为了理解这些认知过程是如何工作的 需要开发描述和分析 大型神经元群体的行为。 This project will use 数学和统计方法来研究的动力学 大量的神经元，特别是集中在 关于单粒子性质的知识扩展问题 神经元及其与完整神经网络的突触连接。

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.