Mathematical Sciences: Modeling of Neural Populations

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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.