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'''Models of neural computation''' are attempts to elucidate, in an abstract and mathematical fashion, the core principles that underlie information processing in biological nervous systems, or functional components thereof. This article aims to provide an overview of the most definitive models of neuro-biological computation as well as the tools commonly used to construct and analyze them.
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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=337–347 |doi= 10.1109/TNSRE.2018.2883618 |pmid=30507514|s2cid=54527064 }}</ref>
===Gain control===
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| title = A New Mechanism for Neuronal Gain Control
|author1=Nicholas J. Priebe |author2=David Ferster
|
| year = 2002
| volume = 35
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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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The Hodgkin–Huxley model, widely regarded as one of the great achievements of 20th-century biophysics, describes how [[action potential]]s in neurons are initiated and propagated in axons via [[voltage-gated ion channel]]s. It is a set of [[nonlinearity|nonlinear]] [[ordinary differential equation]]s that were introduced by [[Alan Lloyd Hodgkin]] and [[Andrew Huxley]] in 1952 to explain the results of [[voltage clamp]] experiments on the [[squid giant axon]]. Analytic solutions do not exist, but the [[Levenberg–Marquardt algorithm]], a modified [[Gauss–Newton algorithm]], is often used to [[curve fitting|fit]] these equations to voltage-clamp data.
The [[FitzHugh–Nagumo model]] is a
====Solitons====
{{main|Soliton model in neuroscience}}
The [[Soliton model in neuroscience|soliton model]] is an alternative to the [[Hodgkin–Huxley model]] that claims to explain how [[action potentials]] are initiated and conducted in the form of certain kinds of [[Solitary wave (water waves)|solitary]] [[sound]] (or [[density]]) pulses that can be modeled as [[soliton]]s along [[axon]]s, based on a thermodynamic theory of nerve pulse propagation.
====Transfer functions and linear filters====
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| pages = 66–78
| doi=10.1093/icb/33.1.66
| doi-access = free
}}</ref><ref>{{cite journal
| doi = 10.2307/1543311
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| pmid = 11341579
| jstor = 1543311
| citeseerx = 10.1.1.116.5190
| s2cid = 18371282
}}</ref>
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| title = Stationary States of the Hartline–Ratliff Model
|author1=K. P. Hadeler |author2=D. Kuhn
|
| year = 1987
| volume = 56
| 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 in sound localization: Jeffress model====
According to [[Lloyd A. Jeffress|Jeffress]],<ref>{{cite journal | last1 = Jeffress | first1 = L.A. | year = 1948 | title = A place theory of sound localization
Following Fischer and Anderson,<ref>{{cite journal | last1 = Fischer | first1 = Brian J. | last2 = Anderson | first2 = Charles H. | year = 2004 | title = A computational model of sound localization in the barn owl
<math>y_{R}\left(t\right) - y_{L}\left(t\right)</math>
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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. |
The master equation for response is
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====Watson–Ahumada model for motion estimation in humans====
This uses a cross-correlation in both the spatial and temporal directions, and is related to the concept of [[optical flow]].<ref>Andrew B. Watson and Albert J. Ahumada, Jr., 1985. Model of human visual-motion sensing "J. Opt. Soc. Am. A" 2(2) 322–341</ref>
===Neurophysiological metronomes: neural circuits for pattern generation===▼
Mutually [[inhibitory]] processes are a unifying motif of all [[central pattern generator]]s. This has been demonstrated in the stomatogastric (STG) nervous system of crayfish and lobsters.<ref>Michael P. Nusbaum and Mark P. Beenhakker, A small-systems approach to motor pattern generation, Nature 417, 343–350 (16 May 2002)</ref> Two and three-cell oscillating networks based on the STG have been constructed which are amenable to mathematical analysis, and which depend in a simple way on synaptic strengths and overall activity, presumably the knobs on these things.<ref>Cristina Soto-Treviño, Kurt A. Thoroughman and Eve Marder, L. F. Abbott, 2006. Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks Nature Vol 4 No 3 2102–2121</ref> The mathematics involved is the theory of [[dynamical systems]].▼
===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
* {{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]] ===
▲====Neurophysiological metronomes: neural circuits for pattern generation====
▲Mutually [[inhibitory]] processes are a unifying motif of all [[central pattern generator]]s. This has been demonstrated in the stomatogastric
====Feedback and control: models of flight control in the fly====
Flight control in the fly is believed to be mediated by inputs from the visual system and also the [[halteres]], a pair of knob-like organs which measure angular velocity. Integrated computer models of ''[[Drosophila]]'', short on neuronal circuitry but based on the general guidelines given by [[control theory]] and data from the tethered flights of flies, have been constructed to investigate the details of flight control.<ref>{{cite web|url=http://strawlab.org/2011/03/23/grand-unified-fly/|title=the Grand Unified Fly (GUF) model
===
[[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 | 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 }}{{dead link|date=July 2022|bot=medic}}{{cbignore|bot=medic}}</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| doi = 10.1016/0306-4522(85)90001-6 | pmid = 4080158| s2cid =10747593 }}</ref>
▲Flight control in the fly is believed to be mediated by inputs from the visual system and also the [[halteres]], a pair of knob-like organs which measure angular velocity. Integrated computer models of ''[[Drosophila]]'', short on neuronal circuitry but based on the general guidelines given by [[control theory]] and data from the tethered flights of flies, have been constructed to investigate the details of flight control.<ref>{{cite web|url=http://strawlab.org/2011/03/23/grand-unified-fly/|title=the Grand Unified Fly (GUF) model|publisher=}}</ref><ref>http://www.mendeley.com/download/public/2464051/3652638122/d3bd7957efd2c8a011afb0687dfb6943731cb6d0/dl.pdf</ref>
==Software modelling approaches and tools==
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<math>f_{j}=\sum_{i}g\left(w_{ji}'x_{i}+b_{j}\right)</math>.
This response is then fed as input into other neurons and so on. The goal is to optimize the weights of the neurons to output a desired response at the output layer respective to a set given inputs at the input layer. This optimization of the neuron weights is often
===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
===NEURON===
The [[Neuron (software)|NEURON]] software, developed at Duke University, is a simulation environment for modeling individual neurons and networks of neurons.<ref>{{cite web|url=http://www.neuron.yale.edu/neuron/|title=NEURON - for empirically-based simulations of neurons and networks of neurons
Twenty years of ModelDB and beyond: building essential modeling tools for the future of neuroscience. J Comput Neurosci. 2017; 42(1):1–10.</ref>
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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
===Retinomorphic chips===
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==See also==
{{div col|
* [[Cognitive architecture]]
* [[Cognitive map]]
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* [[Neuroethology]]
* [[Neuroinformatics]]
* [[Quantitative models of the action potential]]
* [[Spiking neural network]]
* [[Systems neuroscience]]
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==External links==
* [http://www.proberts.net/research/ Neural Dynamics at NSI] – Web page of Patrick D Roberts at the Neurological Sciences Institute
* [http://www.dickinson.caltech.edu/ Dickinson Lab] – Web page of the Dickinson group at Caltech which studies flight control in ''Drosophila''
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{{Neuroethology}}
{{animal cognition}}
▲{{Use dmy dates|date=January 2011}}
{{DEFAULTSORT:Models Of Neural Computation}}
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