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A '''linear''' system is one whose response in a specified unit of measure, to a set of inputs considered at once, is the sum of its responses due to the inputs considered individually.
[[Linear algebra|Linear]] systems are easier to analyze mathematically and are a persuasive assumption in many models including the McCulloch and Pitts neuron, population coding models, and the simple neurons often used in [[Artificial neural network]]s. Linearity may occur in the basic elements of a neural circuit such as the response of a postsynaptic neuron, or as an emergent property of a combination of nonlinear subcircuits.<ref name="MolnarHsueh2009">{{cite journal|last1=Molnar|first1=Alyosha|last2=Hsueh|first2=Hain-Ann|last3=Roska|first3=Botond|last4=Werblin|first4=Frank S.|title=Crossover inhibition in the retina: circuitry that compensates for nonlinear rectifying synaptic transmission|journal=Journal of Computational Neuroscience|volume=27|issue=3|year=2009|pages=569–590|issn=0929-5313|doi=10.1007/s10827-009-0170-6 | pmid = 19636690|pmc=2766457}}</ref> Though linearity is often seen as incorrect, there has been recent work suggesting it may, in fact, be biophysically plausible in some cases.<ref>{{Cite journal|last=Singh|first=Chandan|last2=Levy|first2=William B.|date=2017-07-13|title=A consensus layer V pyramidal neuron can sustain interpulse-interval coding|journal=PLOS ONE|volume=12|issue=7|pages=e0180839|doi=10.1371/journal.pone.0180839|pmid=28704450|pmc=5509228|issn=1932-6203}}</ref><ref>{{Cite journal|last=Cash|first=Sydney|last2=Yuste|first2=Rafael|date=1998-01-01|title=Input Summation by Cultured Pyramidal Neurons Is Linear and Position-Independent|url=http://www.jneurosci.org/content/18/1/10|journal=Journal of Neuroscience|language=en|volume=18|issue=1|pages=10–15|issn=0270-6474|pmid=9412481|doi=10.1523/JNEUROSCI.18-01-00010.1998|doi-access=free}}</ref>
==Examples==
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| doi=10.1093/icb/33.1.66
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| doi = 10.2307/1543311
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===Genetic algorithms===
[[Genetic algorithms]] are used to evolve neural (and sometimes body) properties in a model brain-body-environment system so as to exhibit some desired behavioral performance. The evolved agents can then be subjected to a detailed analysis to uncover their principles of operation. Evolutionary approaches are particularly useful for exploring spaces of possible solutions to a given behavioral task because these approaches minimize a priori assumptions about how a given behavior ought to be instantiated. They can also be useful for exploring different ways to complete a computational neuroethology model when only partial neural circuitry is available for a biological system of interest.<ref>{{cite journal|title=Computational neuroethology|first1=Randall|last1=Beer|first2=Hillel|last2=Chiel|date=4 March 2008|volume=3|issue=3|doi=10.4249/scholarpedia.5307|journal=Scholarpedia|pages=5307|doi-access=free}}</ref>
===NEURON===
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Nervous systems differ from the majority of silicon-based computing devices in that they resemble [[analog computer]]s (not [[digital data]] processors) and massively [[parallel computing|parallel]] processors, not [[von Neumann architecture|sequential]] processors. To model nervous systems accurately, in real-time, alternative hardware is required.
The most realistic circuits to date make use of [[analogue electronics|analog]] properties of existing [[digital electronics]] (operated under non-standard conditions) to realize Hodgkin–Huxley-type models ''in silico''.<ref>L. Alvadoa, J. Tomasa, S. Saghia, S. Renauda, T. Balb, A. Destexheb, G. Le Masson, 2004. Hardware computation of conductance-based neuron models. Neurocomputing 58–60 (2004) 109–115</ref><ref>{{cite journal|title=Silicon neurons|first1=Giacomo|last1=Indiveri|first2=Rodney|last2=Douglas|first3=Leslie|last3=Smith|date=29 March 2008|volume=3|issue=3|doi=10.4249/scholarpedia.1887|journal=Scholarpedia|pages=1887|doi-access=free}}</ref>
===Retinomorphic chips===
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