  A fundamental question in neuroscience is how structure and function of
neural systems are related. We study this interplay by combining a familiar
auto-associative neural network with an evolving mechanism for the birth and
death of synapses. A feedback loop then arises leading to two qualitatively
different types of behaviour. In one, the network structure becomes
heterogeneous and dissasortative, and the system displays good memory
performance; furthermore, the structure is optimised for the particular memory
patterns stored during the process. In the other, the structure remains
homogeneous and incapable of pattern retrieval. These findings provide an
inspiring picture of brain structure and dynamics, are compatible with
experimental results on early brain development, and may help to explain
synaptic pruning. Other evolving networks -- such as those of protein
interaction -- might share the basic ingredients for this feedback loop and
other questions, and indeed many of their structural features are as predicted
by our model.
