Editing Computational neuroscience (section)

===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 usually specific.  It is not known how information is transmitted through such sparsely connected networks, although specific areas of the brain, such as the [[visual cortex]], are understood in some detail.<ref>{{Cite journal|last1=Olshausen|first1=Bruno A.|last2=Field|first2=David J.|date=1997-12-01|title=Sparse coding with an overcomplete basis set: A strategy employed by V1?|journal=Vision Research|volume=37|issue=23|pages=3311–3325|doi=10.1016/S0042-6989(97)00169-7|pmid=9425546|s2cid=14208692|doi-access=free}}</ref> It is also unknown what the computational functions of these specific connectivity patterns are, if any.

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. Some recent evidence suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions.<ref>{{cite journal |vauthors=Schneidman E, Berry MJ, Segev R, Bialek W |title=Weak pairwise correlations imply strongly correlated network states in a neural population |journal=Nature |volume=440 |issue=7087 |pages=1007–12 |year=2006 |pmid=16625187 |pmc=1785327 |doi=10.1038/nature04701 |bibcode=2006Natur.440.1007S|arxiv = q-bio/0512013 }}</ref> It is not known, 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]], which gives rise to the [[Wilson–Cowan model|population model]] of neural networks.<ref>{{cite journal |author1=Wilson, H. R. |author2=Cowan, J.D. |title=A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue 
|journal=Kybernetik |volume=13 |issue=2 |pages=55–80 |year=1973 |doi= 10.1007/BF00288786|pmid=4767470 |s2cid=292546 }}</ref> While many neurotheorists prefer such models with reduced complexity, others argue that uncovering structural-functional relations depends on including as much neuronal and network structure as possible. Models of this type are typically built in large simulation platforms like GENESIS or NEURON. There have been some attempts to provide unified methods that bridge and integrate these levels of complexity.<ref>{{cite book |author1=Anderson, Charles H. |author2=Eliasmith, Chris |title=Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems (Computational Neuroscience) |publisher=The MIT Press |location=Cambridge, Mass |year=2004 |isbn=978-0-262-55060-4 }}</ref>