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Improve the introduction to Inferring interaction graphs.

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Sergiu Ivanov 2022-05-09 10:33:34 +02:00
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scribblings/networks.scrbl
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@ -335,15 +335,16 @@ Build a Boolean network from a given mapping assigning forms to variables.
This section provides inference of both unsigned and signed interaction graphs.
Since the inference of signed interaction graphs is based on analysing the
dynamics of the networks, it may be quite resource-consuming, especially since
I allow any syntactic forms in the definitions of the functions.
any syntactic forms are allowed in the definitions of the functions.
Note the fine difference between @emph{syntactic} interaction graphs and
interaction graphs generated from the dynamics of the network.
Syntactic interaction graphs are based on the whether a variable appears or not
in the form of the function for another variable. On the other hand, the
normal, conventional interaction graph records the fact that one variable has
an impact on the dynamics of the other variable. Depending on the model, these
may or may not be the same.
We use the term @emph{syntactic interaction graph} to refer to the graph in
which the presence of an arc from @tt{x} to @tt{y} is based on whether @tt{x}
appears in the form of @tt{y}. This is quite different from the canonical
definition of the @emph{interaction graph}, in which the arc from @tt{x} to
@tt{y} represents the fact that a change in the value of @tt{x} may lead to
a change in the value of @tt{y}. Thus the syntactic interaction graph may have
extra arcs if @tt{x} appears in the form of @tt{y}, but has no actual influence
on @tt{y}.
@section{Dynamics of networks}