The name is absent



12

Chapter 2

Linear Model Reduction

The focus of this chapter is to introduce linear model reduction techniques by
considering a basic neuronal model and then extending it naturally to a realistic
morphology. Using a single-compartment model, I illustrate the important dynamical
features of neurons. This model is then linearized to obtain the quasi-active model in
order to illustrate subthreshold behavior. Once these concepts have been introduced
in this simple framework, I present the general morphologically accurate model and
proceed with linear model reduction. I demonstrate the efficacy of two techniques,
one dense and one iterative, and discuss their application to various investigations of
behavior in large-scale neurons.

2.1 The Isopotential Cell

One of the most basic isopotential models is the leaky integrate-and-fire (IAF)
model, in which the cell can be modeled as a circuit (see Figure 2.1). Following the
material found in my Master’s thesis (Kellems, 2007), using Kirchhoff’s Current Law,
the change in voltage
v is given by the ordinary differential equation



More intriguing information

1. Studies on association of arbuscular mycorrhizal fungi with gluconacetobacter diazotrophicus and its effect on improvement of sorghum bicolor (L.)
2. Monopolistic Pricing in the Banking Industry: a Dynamic Model
3. The use of formal education in Denmark 1980-1992
4. Kharaj and land proprietary right in the sixteenth century: An example of law and economics
5. The name is absent
6. Voluntary Teaming and Effort
7. Optimal Tax Policy when Firms are Internationally Mobile
8. The ultimate determinants of central bank independence
9. The name is absent
10. SAEA EDITOR'S REPORT, FEBRUARY 1988