Background: Neural modeling is often pursued in an ad hoc way. Researchers add the mechanisms they know about, but need to wave their hands about the ones they don't. They necessarily make many simplifying assumptions but often include many details that are not needed to parsimoniously capture the phenomena. Models depend on parameters, some of which, like the capacitance of the membrane, are known fairly precisely, but others, such as channel densities in the dendrites, are completely unknown. Without better methods, modelers must either make blind guesses about these parameters, or tweak them by hand to get model behavior that seems right. The field of System Identification offers an attempt to provide such better methods. Broadly defined, system ID systematically and rigorously makes inferences about a dynamic system (especially builds a model of the system) based on measured outputs of the system (i.e. based on experimental data). For example, system identification provides tools for validating or falsifying models, estimating their parameters, or choosing between alternative models, based rigorously on experimental data.
In this course, students will become familiar with models of neurons and networks of neurons. Students will learn to use software to translate mathematical models into computer representations for simulation. Finally, students will learn some methods of neural system identification. Specifically, they will learn to estimate the parameters of a model based on data, as well as decide between alternative models based on data. Within this course, for "experimental data," students will use the output of computer simulations (of another model that they will create). While present techniques force the model being fitted to be fairly simple, the model generating the data, like a real neuron, can be quite complicated (or it can be simple). Thus students will test the methods of neural System ID under the realistic assumption that the fitted model does not exactly match the system that generated the data.
As neural system ID is a new field, and as the combinatorics of the possible ways the methods can be tested are staggering, countless original research projects accessible to undergraduates can be formulated. While the primary value of the research will be pedagogical (students will learn modeling and system identification), the projects are of great intellectual interest because they get at epistemological questions concerning what is possible to know about a neuron under any given experimental paradigm (including a "fantasy paradigm" which is possible with simulations, but presently impossible in the lab). I expect to be able to convey my great fascination and enthusiasm for these problems to students.