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===Robustness===
A model is robust if it continues to produce the same computational results under variations in inputs or operating parameters introduced by noise. For example, the direction of motion as computed by a robust [[motion perception|motion detector]] would not change under small changes of [[luminance]], [[contrast (vision)|contrast]] or velocity jitter. For simple mathematical models of neuron, for example the dependence of spike patterns on signal delay is much weaker than the dependence on changes in "weights" of interneuronal connections. <ref>{{cite journal |last1=Cejnar |first1=Pavel |last2=Vyšata |first2=Oldřich |last3=Vališ |first3=Martin |last4=Procházka |first4=Aleš |title=The Complex Behaviour of a Simple Neural Oscillator Model in the Human Cortex |journal=IEEE Transactions on Neural Systems and Rehabilitation Engineering |date=2019 |volume=27 |issue=3 |pages=
===Gain control===
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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|
==Examples==
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| pages = 411–417
| issue = 5–6
| s2cid = 8710876
}}</ref> Assuming these interactions to be '''linear''', they proposed the following relationship for the '''steady-state response rate''' <math>r_p</math> of the given ''p''-th photoreceptor in terms of the steady-state response rates <math>r_j</math> of the ''j'' surrounding receptors:
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====Cross-correlation for motion detection: Hassenstein–Reichardt model====
A motion detector needs to satisfy three general requirements: pair-inputs, asymmetry and nonlinearity.<ref>Borst A, Egelhaaf M., 1989. Principles of visual motion detection. "Trends in Neurosciences" 12(8):297–306</ref> The cross-correlation operation implemented asymmetrically on the responses from a pair of photoreceptors satisfies these minimal criteria, and furthermore, predicts features which have been observed in the response of neurons of the lobula plate in bi-wing insects.<ref>{{cite journal | last1 = Joesch | first1 = M. |display-authors=etal | year = 2008 | title = Response properties of motion-sensitive visual interneurons in the lobula plate of Drosophila melanogaster | url = | journal = Curr. Biol. | volume = 18 | issue = 5| pages = 368–374 | doi=10.1016/j.cub.2008.02.022| pmid = 18328703 | s2cid = 18873331 }}</ref>
The master equation for response is
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===Anti-Hebbian adaptation: spike-timing dependent plasticity===
* {{cite journal | last1 = Tzounopoulos | first1 = T | last2 = Kim | first2 = Y | last3 = Oertel | first3 = D | last4 = Trussell | first4 = LO | year = 2004 | title = Cell-specific, spike timing-dependent plasticities in the dorsal cochlear nucleus | url = | journal = Nat Neurosci | volume = 7 | issue = 7| pages = 719–725 | doi=10.1038/nn1272| pmid = 15208632 | s2cid = 17774457 }}
* {{cite journal | last1 = Roberts | first1 = Patrick D. | last2 = Portfors | first2 = Christine V. | year = 2008 | title = Design principles of sensory processing in cerebellum-like structures| doi = 10.1007/s00422-008-0217-1 | pmid = 18491162 | journal = Biological Cybernetics | volume = 98 | issue = 6| pages = 491–507 | s2cid = 14393814 }}
===Models of [[sensory-motor coupling]] ===
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====Cerebellum sensory motor control====
[[Tensor network theory]] is a theory of [[cerebellum|cerebellar]] function that provides a mathematical model of the [[transformation geometry|transformation]] of sensory [[space-time]] coordinates into motor coordinates and vice versa by cerebellar [[neuronal networks]]. The theory was developed by Andras Pellionisz and [[Rodolfo Llinas]] in the 1980s as a [[geometrization]] of brain function (especially of the [[central nervous system]]) using [[tensor]]s.<ref name="Neuroscience1980-Pellionisz">{{Cite journal| author =Pellionisz, A., Llinás, R. | year =1980 | title =Tensorial Approach To The Geometry Of Brain Function: Cerebellar Coordination Via A Metric Tensor | journal = Neuroscience | volume =5 | issue = 7| pages = 1125––1136 | id = | url= https://www.academia.edu/download/31409354/pellionisz_1980_cerebellar_coordination_via_a_metric_tensor_fullpaper.pdf | doi = 10.1016/0306-4522(80)90191-8 | pmid=6967569| s2cid =17303132 }}</ref><ref name="Neuroscience1985-Pellionisz">{{Cite journal| author = Pellionisz, A., Llinás, R. | year =1985 | title= Tensor Network Theory Of The Metaorganization Of Functional Geometries In The Central Nervous System | journal = Neuroscience | volume =16 | issue =2 | pages = 245–273
==Software modelling approaches and tools==
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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|bibcode=2008SchpJ...3.5307B|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|bibcode=2008SchpJ...3.1887I|doi-access=free}}</ref>
===Retinomorphic chips===
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