Biomedical Engineering Reference
In-Depth Information
nomics, etc.
1
These topics all fall within our initial definition of "complexity,"
though whether they are studied together because of deep connections, or be-
cause of historical accidents and tradition, is a difficult question. In any event,
this chapter will
not
describe the facts and particular models relevant to these
topics.
Instead, this chapter is about the right-hand corner, "tools." Some are proce-
dures for analyzing data, some are for constructing and evaluating models, and
some are for measuring the complexity of data or models. In this chapter I will
restrict myself to methods which are generally accepted as valid (if not always
widely applied),
and
seem promising for biomedical research. These still de-
mand a topic, if not an encyclopedia, rather than a mere chapter! Accordingly, I
will merely try to convey the essentials of the methods, with pointers to refer-
ences for details. The goal is for you to have a sense of which methods would be
good things to try on your problem, rather than to tell you everything you need
to know to implement them.
1.1. Outline of This Chapter
As mentioned above, the techniques of complex systems science can, for
our purposes, be divided into three parts: those for analyzing data (perhaps
without reference to a particular model), those for building and understanding
models (often without data), and those for measuring complexity as such. This
chapter will examine them in that order.
The first part, on
data
, opens with the general ideas of
statistical learning
and data mining
(§2), namely developments in statistics and machine learning
theory that extend statistical methods beyond their traditional domain of low-
dimensional, independent data. We then turn to
time series analysis
(§3), where
there are two important streams of work, inspired by statistics and nonlinear
dynamics.
The second part, on
modeling
, considers the most important and distinctive
classes of models in complex systems. On the vital area of
nonlinear dynamics
,
let the reader consult Socolar (Part II, chapter 2, this volume).
Cellular auto-
mata
(§4) allow us to represent spatial dynamics in a way that is particularly
suited to capturing strong local interactions, spatial heterogeneity, and large-
scale aggregate patterns. Complementary to cellular automata are
agent-based
models
(§5), perhaps the most distinctive and most famous kind of model in
complex systems science. A general section (§6) on
evaluating complex mod-
els
, including analytical methods, various sorts of simulation, and testing, closes
this part of the chapter.
The third part of the chapter considers ways of measuring complexity. As a
necessary preliminary, §7 introduces the concepts of
information theory
, with
some remarks on its application to biological systems. Then §8 treats
complex-
