The name is absent

1.4 Implications for Network Simulations

The results of this thesis have implications beyond just accurate single cell sim-
ulations, and in fact they have profound implications for network simulations. The
overarching goal of network reduction is to model the behavior of a network of cells
with a system of much smaller dimension. It is not as simple as the single-cell case,
however, because often the desired output is an emergent property, meaning that it
arises from the interactions of the many individual cells in the network. One such
output is the mean firing rate of the network, which can be an important feature when
studying brain disorders such as epilepsy. When a network receives too much excita-
tion, or if there is not enough inhibition to counter such excitation, it can fall into a
state of seizure, which is marked by extremely high rates of single cell firing, resulting
in a highly oscillatory network behavior (Traub and Miles, 1991). Understanding how
large networks respond to different input patterns is thus of great importance, but
full-scale simulations can be expensive. It makes sense to look for reduced models
which capture these salient behaviors using many fewer variables and hence which
are faster to simulate.

The network reduction problem has proven to be very difficult and usually has
required assumptions which restrict either the type of cells used, the specific inputs,
or the synaptic connections. All model reduction efforts thus far have also focused on
networks of single-compartment cells. For instance, in 1994 Ermentrout showed that
the firing rate of a network of conductance-based cells can be modeled by a simple

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