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162 G. Polhill

feed-forward network. (If cyclic, the network is recurrent.) Nodes with no input
connections are input nodes; those with no output connections are output nodes.
Since they have no input connections and hence no excitation, input nodes are often
also not given a nonlinear treatment as per (8.3), though this breaks somewhat with
the simulation of a neuron. Similarly, nonlinearity may not be applied to output
nodes. If there are N input nodes, and M output nodes, then essentially a feed-
forward network without nonlinearity on the output nodes is computing a mapping
M
N
M
N
from R to R . With nonlinearity, the mapping is from R to [0, 1] .
Appendix 2: Metrics of and Methods for Validation

Table 8.3 explains various metrics and measures of validation, showing you where
to find out more information on them and how to use them with R. For those
1
of you unfamiliar with R, it is a popularly used free (as in open-source and in
the financial sense) statistical software package, available for Windows, OS-X and
2
Linux. Each of the examples assumes you are validating against a single variable
(unless otherwise stated) for which you have a number of samples from your data
and corresponding output from your model. The R variable vdata contains the
empirical data to validate against (which must not have been used for calibration –
though many of the metrics can of course be applied to the calibration process),
whilst the variable model contains the corresponding output from the model. The
two variables vdata and model are, in R terms, vectors of equal length. If the
model predicted the data perfectly, then for each element i of the two vectors,
vdata[i] DD model[i]. More information on each of the approaches can be found
3
on Wikipedia, R documentation and in various machine learning and advanced
statistical textbooks.

Appendix 3: Expressivity of Various Modelling Approaches

Description logics use a letter-based notation to describe the axioms each logic
has (Baader and Nutt 2003; Calvanese and De Giacomo 2003; Baader et al.
2003). Briefly, AL is a basic description logic, and .D/ is for data properties; C
provides more complex class axioms than the basic axioms in AL; r is for complex
relationship assertions such as irreflexivity (all NetLogo links are irreflexive, e.g. as
you cannot link anything to itself); O introduces nominals (a bit-like enumerations

1
Its popularity in the social simulation community is reflected by the fact that tools have been built
to link it with Wilensky’s (1999) Netlogo (Thiele et al. 2012).
2
http://www.r-project.org/ <Accessed May 2017>.
3 https://www.wikipedia.org/ <Accessed May 2017>.