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Chapter 1

Introduction

In this thesis I present model reduction techniques that can be used to simplify
and accelerate simulations of single neurons and neuronal networks. The fundamental
motivation for pursuing such reductions is the bottleneck created by the large-scale
nature of the problems of theoretical neuroscience. The ultimate goal of this field
is to provide a working model of a realistic brain, but the computational power
required to achieve this end exceeds current technology. Thus, I propose techniques
that shrink the size of the simulated systems while preserving their fidelity to the
originals, thereby allowing current technology to solve problems orders of magnitude
larger than at present.

1.1 Motivation

The brain is the most complicated organ in animals, containing on the order of
IO¹⁰ neurons (of which there are many different types) which are interconnected via
approximately IO¹⁴ synapses (Shepherd and Koch, 1998). From this extraordinarily
complex and heterogeneous network an order emerges whose product is a range of

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