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{{For|the tensor network theory used in quantum physics|Matrix product state}}
'''Tensor network theory''' is a theory of [[brain]] function (particularly that of the [[cerebellum]]) 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}}{{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| url = https://s3.amazonaws.com/academia.edu.documents/31409352/pellionisz_llinas_tensor_tnt_of_metaorganization_1985.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1540567963&Signature=7oENMoA9yBITrBLNf0orulY1uOA%3D&response-content-disposition=inline%3B%20filename%3DTensor_Network_Theory_of_Metaorganizatio.pdf | doi = 10.1016/0306-4522(85)90001-6 | pmid = 4080158}}{{dead link|date=May 2021|bot=medic}}{{cbignore|bot=medic}}</ref>
[[File:Metrictensor.svg|thumb|Metric tensor that transforms input covariant tensors into output contravariant tensors. These tensors can be used to mathematically describe cerebellar neuronal network activities in the central nervous system.]]
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