Behaviors of Networks
Biological neurons are connected to each other in a complex, recurrent fashion. These connections are, unlike most artificial neural networks, sparse and most likely, specific. It is not known how information is transmitted through such sparsely connected networks. It is also unknown what the computational functions, if any, of these specific connectivity patterns are.
The interactions of neurons in a small network can be often reduced to simple models such as the Ising model. The statistical mechanics of such simple systems are well-characterized theoretically. There has been some recent evidence that suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions.(Schneidman et al., 2006; Shlens et al., 2006.) It's unknown, however, whether such descriptive dynamics impart any important computational function. With the emergence of two-photon microscopy and calcium imaging, we now have powerful experimental methods with which to test the new theories regarding neuronal networks.
In some cases the complex interactions between inhibitory and excitatory neurons can be simplified using mean field theory that gives rise to population model of neural networks. While many neuro-theorists prefer such models with reduced complexity, others argue that uncovering structure function relations depends on including as much neuronal and network structure as possible. Models of this type are typically built in large simulations platforms like GENESIS or Neuron. There have been some attempts to provide unified methods that bridge and integrate these levels of complexity.
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