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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|last1=Singh|first1=Chandan|last2=Levy|first2=William B.|date=2017-07-13|title=A consensus layer V pyramidal neuron can sustain interpulse-interval coding|journal=PLOS
==Examples==
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| citeseerx = 10.1.1.116.5190
| s2cid = 18371282
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