Concept Trees: Building Dynamic Concepts from Semi-structured Data Using Nature-Inspired Methods - Complex System Modelling and Control Through Intelligent Soft Computations - page 228

3.5.1 Mathematical Theories

If one considers the natural world, then Cellular Automata might be thought to be
relevant and at some level they provide the required mechanisms. There are dif-
ferent versions of Cellular Automata (Wolfram 1983 , for example). They work
using a localised theory and entropy (Shannon 1948 ) could be a key consideration
for the structure that is described in the following sections. As described in Wi-
kipedia 3 : In thermodynamics, entropy is commonly associated with the amount of
order, disorder, and/or chaos in a thermodynamic system. For a modern interpre-
tation of entropy in statistical mechanics, entropy is the amount of additional
information needed to specify the exact physical state of a system, given its ther-
modynamic speci cation. If thought of as the number of microstates that the system

can take; as a system evolves through exchanges with its environment, or outside
reservoir, through energy, volume or molecules, for example; the entropy will
increase to a maximum and equilibrium value. The information that speci

es the
system will evolve to the maximum amount. As the microstates are realised, the
system achieves its minimum potential for change, or best entropy state. In infor-
mation theory, entropy is a measure of the uncertainty in information content, or the
amount of unpredictability in a random variable (Shannon 1948 ). As more certainty
about the information source is achieved, the entropy (potential uncertainty)
reduces, to a minimum and more balanced amount.
However, it would be dif

cult to map these types of state machine, or mini-
computers, over to a process that is designed only to link up text, to create
ontologies. Most distributed systems use some kind of localised theory as well, in
any case. The reason for this section is the fact that the dynamic linking uses a basic
association equation to create links and also, as described later, makes a decision
about breaking a link and creating a new structure. To show their relation to
distributed systems and nature, the following quote is from the start of the paper
(Wolfram 1983 ).

It appears that the basic laws of physics relevant to everyday phenomena are now known.
Yet there are many everyday natural systems whose complex structure and behaviour have
so far defied even qualitative analysis. For example, the laws that govern the freezing of
water and the conduction of heat have long been known, but analysing their consequences
for the intricate patterns of snow ake growth has not yet been possible. While many

complex systems may be broken down into identical components, each obeying simple
laws, the huge number of components that make up the whole system act together to yield
very complex behaviour.

fl

If we know what the underlying theory of the system is, then it can build itself in
a distributed manner, even if we do not know what the eventual structure will be.
Cellular Automata would be too rigid for a concept tree, as they can be created from
a fixed grid structure with local interactions only; while a concept tree is required to

3 http://en.wikipedia.org/wiki/Entropy , plus_(information_theory), _(statistical_thermo-dynam-
ics), or _(order_and_disorder), for example.