# Tensorial approach to the geometry of brain function: Cerebellar coordination via a metric tensor

@article{Pellionisz1980TensorialAT, title={Tensorial approach to the geometry of brain function: Cerebellar coordination via a metric tensor}, author={A. J. Pellionisz and Rodolfo R. Llin{\'a}s}, journal={Neuroscience}, year={1980}, volume={5}, pages={1125-1136} }

## 360 Citations

Geometrical approach to neural net control of movements and posture.

- Computer ScienceProgress in brain research
- 1993

Tensor network theory of the metaorganization of functional geometries in the central nervous system

- Computer ScienceNeuroscience
- 1985

Tensor geometry: a language of brains & neurocomputers. Generalized coordinates in neuroscience & robotics

- Computer Science
- 1988

Utilizations of the tensor approach center on natural and artificial sensorimotor operations, promoting a co-evolution of coordinated (and intelligent) robots with Nature’s systems such as adaptive cerebellar compensatory reflexes.

Tensor Theory of Brain Function. The Cerebellum as a Space-Time Metric

- Biology
- 1982

The Tensor Network Theory of Central Nervous System (a geometrical abstraction and generalization of the known vector-matrix approaches) is capable of yielding a usable understanding and a tensorial network model capable of generating motor coordination via cerebellar-type neuronal circuits is offered.

Coordination: a vector-matrix description of transformations of overcomplete CNS coordinates and a tensorial solution using the Moore-Penrose generalized inverse.

- Computer ScienceJournal of theoretical biology
- 1984

Space-time representation in the brain. The cerebellum as a predictive space-time metric tensor

- Computer ScienceNeuroscience
- 1982

Sensori-motor transformations in the brain (with a critique of the tensor theory of cerebellum).

- BiologyJournal of theoretical biology
- 1985

Tensorial aspects of the multidimensional massively parallel sensorimotor function of neuronal networks.

- Biology, PsychologyProgress in brain research
- 1988

Tensorial computer model of gaze—I. Oculomotor activity is expressed in non-orthogonal natural coordinates

- BiologyNeuroscience
- 1985

Distributed parallel processing in the vertical vestibulo-ocular reflex: Learning networks compared to tensor theory

- BiologyBiological Cybernetics
- 2004

This work modeled the vertical VOR as a three-layered neural network programmed using the back-propagation learning algorithm and demonstrated how vestibular nucleus neurons can encode the VOR sensorimotor transformation in a distributed manner.

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